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| mathematical statistics and applications: Mathematical Statistics with Applications Kandethody M. Ramachandran, Chris P. Tsokos, 2009-03-13 Mathematical Statistics with Applications provides a calculus-based theoretical introduction to mathematical statistics while emphasizing interdisciplinary applications as well as exposure to modern statistical computational and simulation concepts that are not covered in other textbooks. Includes the Jackknife, Bootstrap methods, the EM algorithms and Markov chain Monte Carlo methods. Prior probability or statistics knowledge is not required. Step-by-step procedure to solve real problems, making the topic more accessible Exercises blend theory and modern applications Practical, real-world chapter projects Provides an optional section in each chapter on using Minitab, SPSS and SAS commands |
| mathematical statistics and applications: Modern Mathematical Statistics with Applications Jay L. Devore, Kenneth N. Berk, 2011-12-07 Modern Mathematical Statistics with Applications, Second Edition strikes a balance between mathematical foundations and statistical practice. In keeping with the recommendation that every math student should study statistics and probability with an emphasis on data analysis, accomplished authors Jay Devore and Kenneth Berk make statistical concepts and methods clear and relevant through careful explanations and a broad range of applications involving real data. The main focus of the book is on presenting and illustrating methods of inferential statistics that are useful in research. It begins with a chapter on descriptive statistics that immediately exposes the reader to real data. The next six chapters develop the probability material that bridges the gap between descriptive and inferential statistics. Point estimation, inferences based on statistical intervals, and hypothesis testing are then introduced in the next three chapters. The remainder of the book explores the use of this methodology in a variety of more complex settings. This edition includes a plethora of new exercises, a number of which are similar to what would be encountered on the actuarial exams that cover probability and statistics. Representative applications include investigating whether the average tip percentage in a particular restaurant exceeds the standard 15%, considering whether the flavor and aroma of Champagne are affected by bottle temperature or type of pour, modeling the relationship between college graduation rate and average SAT score, and assessing the likelihood of O-ring failure in space shuttle launches as related to launch temperature. |
| mathematical statistics and applications: Mathematical Statistics with Applications Dennis D. Wackerly, William Mendenhall, Richard L. Scheaffer, 2008 The authors present the theory of statistics in the context of practical problem solving and real world applications. This practical approach helps you discover the nature of statistics and comprehend its essential role in scientific research.-- |
| mathematical statistics and applications: Stat Labs Deborah Nolan, Terry P. Speed, 2006-05-02 Integrating the theory and practice of statistics through a series of case studies, each lab introduces a problem, provides some scientific background, suggests investigations for the data, and provides a summary of the theory used in each case. Aimed at upper-division students. |
| mathematical statistics and applications: Probability and Mathematical Statistics Mary C. Meyer, 2019-06-24 This book develops the theory of probability and mathematical statistics with the goal of analyzing real-world data. Throughout the text, the R package is used to compute probabilities, check analytically computed answers, simulate probability distributions, illustrate answers with appropriate graphics, and help students develop intuition surrounding probability and statistics. Examples, demonstrations, and exercises in the R programming language serve to reinforce ideas and facilitate understanding and confidence. The books Chapter Highlights provide a summary of key concepts, while the examples utilizing R within the chapters are instructive and practical. Exercises that focus on real-world applications without sacrificing mathematical rigor are included, along with more than 200 figures that help clarify both concepts and applications. In addition, the book features two helpful appendices: annotated solutions to 700 exercises and a Review of Useful Math. Written for use in applied masters classes, Probability and Mathematical Statistics: Theory, Applications, and Practice in R is also suitable for advanced undergraduates and for self-study by applied mathematicians and statisticians and qualitatively inclined engineers and scientists. |
| mathematical statistics and applications: Introduction to Probability and Mathematical Statistics Lee J. Bain, Max Engelhardt, 2000-03-01 The Second Edition of INTRODUCTION TO PROBABILITY AND MATHEMATICAL STATISTICS focuses on developing the skills to build probability (stochastic) models. Lee J. Bain and Max Engelhardt focus on the mathematical development of the subject, with examples and exercises oriented toward applications. |
| mathematical statistics and applications: Mathematical Statistics With Applications Asha Seth Kapadia, Wenyaw Chan, Lemuel A. Moyé, 2017-07-12 Mathematical statistics typically represents one of the most difficult challenges in statistics, particularly for those with more applied, rather than mathematical, interests and backgrounds. Most textbooks on the subject provide little or no review of the advanced calculus topics upon which much of mathematical statistics relies and furthermore contain material that is wholly theoretical, thus presenting even greater challenges to those interested in applying advanced statistics to a specific area. Mathematical Statistics with Applications presents the background concepts and builds the technical sophistication needed to move on to more advanced studies in multivariate analysis, decision theory, stochastic processes, or computational statistics. Applications embedded within theoretical discussions clearly demonstrate the utility of the theory in a useful and relevant field of application and allow readers to avoid sudden exposure to purely theoretical materials. With its clear explanations and more than usual emphasis on applications and computation, this text reaches out to the many students and professionals more interested in the practical use of statistics to enrich their work in areas such as communications, computer science, economics, astronomy, and public health. |
| mathematical statistics and applications: Mathematical Statistics with Resampling and R Laura M. Chihara, Tim C. Hesterberg, 2018-09-17 This thoroughly updated second edition combines the latest software applications with the benefits of modern resampling techniques Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. The second edition of Mathematical Statistics with Resampling and R combines modern resampling techniques and mathematical statistics. This book has been classroom-tested to ensure an accessible presentation, uses the powerful and flexible computer language R for data analysis and explores the benefits of modern resampling techniques. This book offers an introduction to permutation tests and bootstrap methods that can serve to motivate classical inference methods. The book strikes a balance between theory, computing, and applications, and the new edition explores additional topics including consulting, paired t test, ANOVA and Google Interview Questions. Throughout the book, new and updated case studies are included representing a diverse range of subjects such as flight delays, birth weights of babies, and telephone company repair times. These illustrate the relevance of the real-world applications of the material. This new edition: • Puts the focus on statistical consulting that emphasizes giving a client an understanding of data and goes beyond typical expectations • Presents new material on topics such as the paired t test, Fisher's Exact Test and the EM algorithm • Offers a new section on Google Interview Questions that illustrates statistical thinking • Provides a new chapter on ANOVA • Contains more exercises and updated case studies, data sets, and R code Written for undergraduate students in a mathematical statistics course as well as practitioners and researchers, the second edition of Mathematical Statistics with Resampling and R presents a revised and updated guide for applying the most current resampling techniques to mathematical statistics. |
| mathematical statistics and applications: An Introduction to Mathematical Statistics and Its Applications Richard J. Larsen, Morris L. Marx, 2012 Offering comprehensive coverage of the theoretical aspects of mathematical statistics, this text demonstrates how and when to use statistical methods, while reinforcing the calculus that students will have mastered in previous courses. |
| mathematical statistics and applications: Mathematical Statistics Jun Shao, 2008-02-03 This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are useful in statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Chapters 3-7 contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each chapter provide not only practice problems for students, but also many additional results. In addition to improving the presentation, the new edition makes Chapter 1 a self-contained chapter for probability theory with emphasis in statistics. Added topics include useful moment inequalities, more discussions of moment generating and characteristic functions, conditional independence, Markov chains, martingales, Edgeworth and Cornish-Fisher expansions, and proofs to many key theorems such as the dominated convergence theorem, monotone convergence theorem, uniqueness theorem, continuity theorem, law of large numbers, and central limit theorem. A new section in Chapter 5 introduces semiparametric models, and a number of new exercises were added to each chapter. |
| mathematical statistics and applications: The Application of Mathematical Statistics to Chemical Analysis V. V. Nalimov, 2014-05-09 The Application of Mathematical Statistics to Chemical Analysis presents the methods of mathematical statistics as applied to problems connected with chemical analysis. This book is divided into nine chapters that particularly consider the principal theorems of mathematical statistics that are explained with examples taken from researchers associated with chemical analysis in laboratory work. This text deals first with the problems of mathematical statistics as a means to summarize information in chemical analysis. The next chapters examine the classification of errors, random variables and their characteristics, and the normal distribution in mathematical statistics. These topics are followed by surveys of the application of Poisson's and binomial distribution in radiochemical analysis; the estimation of chemical analytic results; and the principles and application of determination of experimental variance. The last chapters explore the determination of statistical parameters of linear relations and some working methods associated with the statistical design of an experiment. This book will be of great value to analytical chemists and mathematical statisticians. |
| mathematical statistics and applications: Fundamentals of Mathematical Statistics S.C. Gupta, V.K. Kapoor, 2020-09-10 Knowledge updating is a never-ending process and so should be the revision of an effective textbook. The book originally written fifty years ago has, during the intervening period, been revised and reprinted several times. The authors have, however, been thinking, for the last few years that the book needed not only a thorough revision but rather a substantial rewriting. They now take great pleasure in presenting to the readers the twelfth, thoroughly revised and enlarged, Golden Jubilee edition of the book. The subject-matter in the entire book has been re-written in the light of numerous criticisms and suggestions received from the users of the earlier editions in India and abroad. The basis of this revision has been the emergence of new literature on the subject, the constructive feedback from students and teaching fraternity, as well as those changes that have been made in the syllabi and/or the pattern of examination papers of numerous universities. Knowledge updating is a never-ending process and so should be the revision of an effective textbook. The book originally written fifty years ago has, during the intervening period, been revised and reprinted several times. The authors have, however, been thinking, for the last few years that the book needed not only a thorough revision but rather a substantial rewriting. They now take great pleasure in presenting to the readers the twelfth, thoroughly revised and enlarged, Golden Jubilee edition of the book. The subject-matter in the entire book has been re-written in the light of numerous criticisms and suggestions received from the users of the earlier editions in India and abroad. The basis of this revision has been the emergence of new literature on the subject, the constructive feedback from students and teaching fraternity, as well as those changes that have been made in the syllabi and/or the pattern of examination papers of numerous universities. Knowledge updating is a never-ending process and so should be the revision of an effective textbook. The book originally written fifty years ago has, during the intervening period, been revised and reprinted several times. The authors have, however, been thinking, for the last few years that the book needed not only a thorough revision but rather a substantial rewriting. They now take great pleasure in presenting to the readers the twelfth, thoroughly revised and enlarged, Golden Jubilee edition of the book. The subject-matter in the entire book has been re-written in the light of numerous criticisms and suggestions received from the users of the earlier editions in India and abroad. The basis of this revision has been the emergence of new literature on the subject, the constructive feedback from students and teaching fraternity, as well as those changes that have been made in the syllabi and/or the pattern of examination papers of numerous universities. Some prominent additions are given below: 1. Variance of Degenerate Random Variable 2. Approximate Expression for Expectation and Variance 3. Lyapounov’s Inequality 4. Holder’s Inequality 5. Minkowski’s Inequality 6. Double Expectation Rule or Double-E Rule and many others |
| mathematical statistics and applications: John E. Freund's Mathematical Statistics with Applications Irwin Miller, Marylees Miller, John E. Freund, 2014 John E. Freund's Mathematical Statistics with Applications , Eighth Edition, provides a calculus-based introduction to the theory and application of statistics, based on comprehensive coverage that reflects the latest in statistical thinking, the teaching of statistics, and current practices. |
| mathematical statistics and applications: All of Statistics Larry Wasserman, 2004-09-17 This book is for people who want to learn probability and statistics quickly. It brings together many of the main ideas in modern statistics in one place. The book is suitable for students and researchers in statistics, computer science, data mining and machine learning. This book covers a much wider range of topics than a typical introductory text on mathematical statistics. It includes modern topics like nonparametric curve estimation, bootstrapping and classification, topics that are usually relegated to follow-up courses. The reader is assumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. The text can be used at the advanced undergraduate and graduate level. Larry Wasserman is Professor of Statistics at Carnegie Mellon University. He is also a member of the Center for Automated Learning and Discovery in the School of Computer Science. His research areas include nonparametric inference, asymptotic theory, causality, and applications to astrophysics, bioinformatics, and genetics. He is the 1999 winner of the Committee of Presidents of Statistical Societies Presidents' Award and the 2002 winner of the Centre de recherches mathematiques de Montreal–Statistical Society of Canada Prize in Statistics. He is Associate Editor of The Journal of the American Statistical Association and The Annals of Statistics. He is a fellow of the American Statistical Association and of the Institute of Mathematical Statistics. |
| mathematical statistics and applications: Mathematical Statistics Keith Knight, 1999-11-24 Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow students to understand the theoretical underpinnings of statistical methodology. The author concentrates on inferential procedures within the framework of parametric models, but - acknowledging that models are often incorrectly specified - he also views estimation from a non-parametric perspective. Overall, Mathematical Statistics places greater emphasis on frequentist methodology than on Bayesian, but claims no particular superiority for that approach. It does emphasize, however, the utility of statistical and mathematical software packages, and includes several sections addressing computational issues. The result reaches beyond nice mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry. |
| mathematical statistics and applications: Mathematical Statistics with Mathematica Colin Rose, Murray D. Smith, 2002 This text and software package presents a unified approach for doing mathematical statistics with Mathematica. The mathStatica software empowers the student with the ability to solve difficult problems. The professional statistician should be able to tackle tricky multivariate distributions, generating functions, inversion theorems, symbolic maximum likelihood estimation, unbiased estimation, and the checking and correcting of textbook formulae. This is the ideal companion for researchers and students in statistics, econometrics, engineering, physics, psychometrics, economics, finance, biometrics, and the social sciences. The mathStatica CD-ROM includes: mathStatica - the applications pack for mathematical statistics, custom Mathematica palettes, live interactive book that is identical to the printed text, online help, and a trial version of Mathematica 4.0. |
| mathematical statistics and applications: Mathematical Statistics Dieter Rasch, Dieter Schott, 2018-01-09 Explores mathematical statistics in its entirety—from the fundamentals to modern methods This book introduces readers to point estimation, confidence intervals, and statistical tests. Based on the general theory of linear models, it provides an in-depth overview of the following: analysis of variance (ANOVA) for models with fixed, random, and mixed effects; regression analysis is also first presented for linear models with fixed, random, and mixed effects before being expanded to nonlinear models; statistical multi-decision problems like statistical selection procedures (Bechhofer and Gupta) and sequential tests; and design of experiments from a mathematical-statistical point of view. Most analysis methods have been supplemented by formulae for minimal sample sizes. The chapters also contain exercises with hints for solutions. Translated from the successful German text, Mathematical Statistics requires knowledge of probability theory (combinatorics, probability distributions, functions and sequences of random variables), which is typically taught in the earlier semesters of scientific and mathematical study courses. It teaches readers all about statistical analysis and covers the design of experiments. The book also describes optimal allocation in the chapters on regression analysis. Additionally, it features a chapter devoted solely to experimental designs. Classroom-tested with exercises included Practice-oriented (taken from day-to-day statistical work of the authors) Includes further studies including design of experiments and sample sizing Presents and uses IBM SPSS Statistics 24 for practical calculations of data Mathematical Statistics is a recommended text for advanced students and practitioners of math, probability, and statistics. |
| mathematical statistics and applications: Foundations and Applications of Statistics Randall Pruim, 2018-04-04 Foundations and Applications of Statistics simultaneously emphasizes both the foundational and the computational aspects of modern statistics. Engaging and accessible, this book is useful to undergraduate students with a wide range of backgrounds and career goals. The exposition immediately begins with statistics, presenting concepts and results from probability along the way. Hypothesis testing is introduced very early, and the motivation for several probability distributions comes from p-value computations. Pruim develops the students' practical statistical reasoning through explicit examples and through numerical and graphical summaries of data that allow intuitive inferences before introducing the formal machinery. The topics have been selected to reflect the current practice in statistics, where computation is an indispensible tool. In this vein, the statistical computing environment R is used throughout the text and is integral to the exposition. Attention is paid to developing students' mathematical and computational skills as well as their statistical reasoning. Linear models, such as regression and ANOVA, are treated with explicit reference to the underlying linear algebra, which is motivated geometrically. Foundations and Applications of Statistics discusses both the mathematical theory underlying statistics and practical applications that make it a powerful tool across disciplines. The book contains ample material for a two-semester course in undergraduate probability and statistics. A one-semester course based on the book will cover hypothesis testing and confidence intervals for the most common situations. In the second edition, the R code has been updated throughout to take advantage of new R packages and to illustrate better coding style. New sections have been added covering bootstrap methods, multinomial and multivariate normal distributions, the delta method, numerical methods for Bayesian inference, and nonlinear least squares. Also, the use of matrix algebra has been expanded, but remains optional, providing instructors with more options regarding the amount of linear algebra required. |
| mathematical statistics and applications: Mathematical Statistics with Applications in R Kandethody M. Ramachandran, Chris P. Tsokos, 2020-05-14 Mathematical Statistics with Applications in R, Third Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods, such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem-solving in a logical manner. Step-by-step procedure to solve real problems make the topics very accessible. - Presents step-by-step procedures to solve real problems, making each topic more accessible - Provides updated application exercises in each chapter, blending theory and modern methods with the use of R - Includes new chapters on Categorical Data Analysis and Extreme Value Theory with Applications - Wide array coverage of ANOVA, Nonparametric, Bayesian and empirical methods |
| mathematical statistics and applications: Probability and Statistics with Applications: A Problem Solving Text Leonard Asimow, Ph.D., ASA, Mark Maxwell, Ph.D., ASA, 2015-06-30 This text is listed on the Course of Reading for SOA Exam P. Probability and Statistics with Applications is an introductory textbook designed to make the subject accessible to college freshmen and sophomores concurrent with Calc II and III, with a prerequisite of just one smester of calculus. It is organized specifically to meet the needs of students who are preparing for the Society of Actuaries qualifying Examination P and Casualty Actuarial Society's new Exam S. Sample actuarial exam problems are integrated throughout the text along with an abundance of illustrative examples and 870 exercises. The book provides the content to serve as the primary text for a standard two-semester advanced undergraduate course in mathematical probability and statistics. 2nd Edition Highlights Expansion of statistics portion to cover CAS ST and all of the statistics portion of CAS SAbundance of examples and sample exam problems for both Exams SOA P and CAS SCombines best attributes of a solid text and an actuarial exam study manual in one volumeWidely used by college freshmen and sophomores to pass SOA Exam P early in their college careersMay be used concurrently with calculus coursesNew or rewritten sections cover topics such as discrete and continuous mixture distributions, non-homogeneous Poisson processes, conjugate pairs in Bayesian estimation, statistical sufficiency, non-parametric statistics, and other topics also relevant to SOA Exam C. |
| mathematical statistics and applications: Applications of Measure Theory to Statistics Gogi Pantsulaia, 2016-12-22 This book aims to put strong reasonable mathematical senses in notions of objectivity and subjectivity for consistent estimations in a Polish group by using the concept of Haar null sets in the corresponding group. This new approach – naturally dividing the class of all consistent estimates of an unknown parameter in a Polish group into disjoint classes of subjective and objective estimates – helps the reader to clarify some conjectures arising in the criticism of null hypothesis significance testing. The book also acquaints readers with the theory of infinite-dimensional Monte Carlo integration recently developed for estimation of the value of infinite-dimensional Riemann integrals over infinite-dimensional rectangles. The book is addressed both to graduate students and to researchers active in the fields of analysis, measure theory, and mathematical statistics. |
| mathematical statistics and applications: Mathematical Statistics for Applied Econometrics Charles B Moss, 2014-10-16 An Introductory Econometrics Text Mathematical Statistics for Applied Econometrics covers the basics of statistical inference in support of a subsequent course on classical econometrics. The book shows students how mathematical statistics concepts form the basis of econometric formulations. It also helps them think about statistics as more than a toolbox of techniques. Uses Computer Systems to Simplify Computation The text explores the unifying themes involved in quantifying sample information to make inferences. After developing the necessary probability theory, it presents the concepts of estimation, such as convergence, point estimators, confidence intervals, and hypothesis tests. The text then shifts from a general development of mathematical statistics to focus on applications particularly popular in economics. It delves into matrix analysis, linear models, and nonlinear econometric techniques. Students Understand the Reasons for the Results Avoiding a cookbook approach to econometrics, this textbook develops students’ theoretical understanding of statistical tools and econometric applications. It provides them with the foundation for further econometric studies. |
| mathematical statistics and applications: Statistics for High-Dimensional Data Peter Bühlmann, Sara van de Geer, 2011-06-08 Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science. |
| mathematical statistics and applications: Mathematical Statistics with Applications Dennis Wackerly, William Mendenhall, Richard L. Scheaffer, 2014-10-27 In their bestselling MATHEMATICAL STATISTICS WITH APPLICATIONS, premiere authors Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors' use of practical applications and excellent exercises helps students discover the nature of statistics and understand its essential role in scientific research. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. |
| mathematical statistics and applications: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site. |
| mathematical statistics and applications: Mathematical Statistics Richard J. Rossi, 2018-06-14 Presents a unified approach to parametric estimation, confidence intervals, hypothesis testing, and statistical modeling, which are uniquely based on the likelihood function This book addresses mathematical statistics for upper-undergraduates and first year graduate students, tying chapters on estimation, confidence intervals, hypothesis testing, and statistical models together to present a unifying focus on the likelihood function. It also emphasizes the important ideas in statistical modeling, such as sufficiency, exponential family distributions, and large sample properties. Mathematical Statistics: An Introduction to Likelihood Based Inference makes advanced topics accessible and understandable and covers many topics in more depth than typical mathematical statistics textbooks. It includes numerous examples, case studies, a large number of exercises ranging from drill and skill to extremely difficult problems, and many of the important theorems of mathematical statistics along with their proofs. In addition to the connected chapters mentioned above, Mathematical Statistics covers likelihood-based estimation, with emphasis on multidimensional parameter spaces and range dependent support. It also includes a chapter on confidence intervals, which contains examples of exact confidence intervals along with the standard large sample confidence intervals based on the MLE's and bootstrap confidence intervals. There’s also a chapter on parametric statistical models featuring sections on non-iid observations, linear regression, logistic regression, Poisson regression, and linear models. Prepares students with the tools needed to be successful in their future work in statistics data science Includes practical case studies including real-life data collected from Yellowstone National Park, the Donner party, and the Titanic voyage Emphasizes the important ideas to statistical modeling, such as sufficiency, exponential family distributions, and large sample properties Includes sections on Bayesian estimation and credible intervals Features examples, problems, and solutions Mathematical Statistics: An Introduction to Likelihood Based Inference is an ideal textbook for upper-undergraduate and graduate courses in probability, mathematical statistics, and/or statistical inference. |
| mathematical statistics and applications: Mathematical Statistics and Data Analysis John A. Rice, 2007 This is the first text in a generation to re-examine the purpose of the mathematical statistics course. The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts that are set in abstract settings. |
| mathematical statistics and applications: An Introduction to Mathematical Statistics Fetsje Bijma, Marianne Jonker, A. W. van der Vaart, 2017 This book gives an introduction into mathematical statistics. |
| mathematical statistics and applications: A Course in Mathematical Statistics and Large Sample Theory Rabi Bhattacharya, Lizhen Lin, Victor Patrangenaru, 2016-08-13 This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods. |
| mathematical statistics and applications: Mathematical Statistics A A Borokov, 1999-01-27 A wide-ranging, extensive overview of modern mathematical statistics, this work reflects the current state of the field while being succinct and easy to grasp. The mathematical presentation is coherent and rigorous throughout. The author presents classical results and methods that form the basis of modern statistics, and examines the foundations of estimation theory, hypothesis testing theory and statistical game theory. He then considers statistical problems for two or more samples, and those in which observations are taken from different distributions. Methods of finding optimal and asymptotically optimal statistical procedures are given, along with treatments of homogeneity testing, regression, variance analysis and pattern recognition. The author also posits a number of methodological improvements that simplify proofs, and brings together a number of new results which have never before been published in a single monograph. |
| mathematical statistics and applications: Random Integral Equations with Applications to Life Sciences and Engineering , 1974-08-20 In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering |
| mathematical statistics and applications: Probability and Statistics Gunnar Blom, 2012-12-06 This is a somewhat extended and modified translation of the third edition of the text, first published in 1969. The Swedish edition has been used for many years at the Royal Institute of Technology in Stockholm, and at the School of Engineering at Link6ping University. It is also used in elementary courses for students of mathematics and science. The book is not intended for students interested only in theory, nor is it suited for those seeking only statistical recipes. Indeed, it is designed to be intermediate between these extremes. I have given much thought to the question of dividing the space, in an appropriate way, between mathematical arguments and practical applications. Mathematical niceties have been left aside entirely, and many results are obtained by analogy. The students I have in mind should have three ingredients in their course: elementary probability theory with applications, statistical theory with applications, and something about the planning of practical investiga tions. When pouring these three ingredients into the soup, I have tried to draw upon my experience as a university teacher and on my earlier years as an industrial statistician. The programme may sound bold, and the reader should not expect too much from this book. Today, probability, statistics and the planning of investigations cover vast areas and, in 356 pages, only the most basic problems can be discussed. If the reader gains a good understanding of probabilistic and statistical reasoning, the main purpose of the book has been fulfilled. |
| mathematical statistics and applications: Mathematical Methods of Statistics Harald Cramér, 1999-04-12 In this classic of statistical mathematical theory, Harald Cram r joins the two major lines of development in the field: while British and American statisticians were developing the science of statistical inference, French and Russian probabilitists transformed the classical calculus of probability into a rigorous and pure mathematical theory. The result of Cram r's work is a masterly exposition of the mathematical methods of modern statistics that set the standard that others have since sought to follow. For anyone with a working knowledge of undergraduate mathematics the book is self contained. The first part is an introduction to the fundamental concept of a distribution and of integration with respect to a distribution. The second part contains the general theory of random variables and probability distributions while the third is devoted to the theory of sampling, statistical estimation, and tests of significance. |
| mathematical statistics and applications: Mathematical Statistics for Economics and Business Ron C. Mittelhammer, 2015-04-02 Mathematical Statistics for Economics and Business, Second Edition, provides a comprehensive introduction to the principles of mathematical statistics which underpin statistical analyses in the fields of economics, business, and econometrics. The selection of topics in this textbook is designed to provide students with a conceptual foundation that will facilitate a substantial understanding of statistical applications in these subjects. This new edition has been updated throughout and now also includes a downloadable Student Answer Manual containing detailed solutions to half of the over 300 end-of-chapter problems. After introducing the concepts of probability, random variables, and probability density functions, the author develops the key concepts of mathematical statistics, most notably: expectation, sampling, asymptotics, and the main families of distributions. The latter half of the book is then devoted to the theories of estimation and hypothesis testing with associated examples and problems that indicate their wide applicability in economics and business. Features of the new edition include: a reorganization of topic flow and presentation to facilitate reading and understanding; inclusion of additional topics of relevance to statistics and econometric applications; a more streamlined and simple-to-understand notation for multiple integration and multiple summation over general sets or vector arguments; updated examples; new end-of-chapter problems; a solution manual for students; a comprehensive answer manual for instructors; and a theorem and definition map. This book has evolved from numerous graduate courses in mathematical statistics and econometrics taught by the author, and will be ideal for students beginning graduate study as well as for advanced undergraduates. |
| mathematical statistics and applications: Student Solutions Manual for Wackerly/Mendenhall/Scheaffer's Mathematical Statistics with Applications, 7th Dennis Wackerly, William J. Owen, William Mendenhall, Richard L. Scheaffer, 2007-09 Prepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring worked out-solutions to the problems in MATHEMATICAL STATISTICS WITH APPLICATIONS, 7th Edition, this manual shows you how to approach and solve problems using the same step-by-step explanations found in your textbook examples. |
| mathematical statistics and applications: Statistics and Probability with Applications (High School) Daren Starnes, Josh Tabor, 2016-10-07 Statistics and Probability with Applications, Third Edition is the only introductory statistics text written by high school teachers for high school teachers and students. Daren Starnes, Josh Tabor, and the extended team of contributors bring their in-depth understanding of statistics and the challenges faced by high school students and teachers to development of the text and its accompanying suite of print and interactive resources for learning and instruction. A complete re-envisioning of the authors’ Statistics Through Applications, this new text covers the core content for the course in a series of brief, manageable lessons, making it easy for students and teachers to stay on pace. Throughout, new pedagogical tools and lively real-life examples help captivate students and prepare them to use statistics in college courses and in any career. |
| mathematical statistics and applications: Stat Labs Deborah Nolan, Terry P. Speed, 2001-11-26 Integrating the theory and practice of statistics through a series of case studies, each lab introduces a problem, provides some scientific background, suggests investigations for the data, and provides a summary of the theory used in each case. Aimed at upper-division students. |
| mathematical statistics and applications: Classic Topics on the History of Modern Mathematical Statistics Prakash Gorroochurn, 2016-04-04 There is nothing like it on the market...no others are as encyclopedic...the writing is exemplary: simple, direct, and competent. —George W. Cobb, Professor Emeritus of Mathematics and Statistics, Mount Holyoke College Written in a direct and clear manner, Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times presents a comprehensive guide to the history of mathematical statistics and details the major results and crucial developments over a 200-year period. Presented in chronological order, the book features an account of the classical and modern works that are essential to understanding the applications of mathematical statistics. Divided into three parts, the book begins with extensive coverage of the probabilistic works of Laplace, who laid much of the foundations of later developments in statistical theory. Subsequently, the second part introduces 20th century statistical developments including work from Karl Pearson, Student, Fisher, and Neyman. Lastly, the author addresses post-Fisherian developments. Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times also features: A detailed account of Galton's discovery of regression and correlation as well as the subsequent development of Karl Pearson's X2 and Student's t A comprehensive treatment of the permeating influence of Fisher in all aspects of modern statistics beginning with his work in 1912 Significant coverage of Neyman–Pearson theory, which includes a discussion of the differences to Fisher’s works Discussions on key historical developments as well as the various disagreements, contrasting information, and alternative theories in the history of modern mathematical statistics in an effort to provide a thorough historical treatment Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times is an excellent reference for academicians with a mathematical background who are teaching or studying the history or philosophical controversies of mathematics and statistics. The book is also a useful guide for readers with a general interest in statistical inference. |
Mathematics - Wikipedia
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
Wolfram Mathematica: Modern Technical Computing
Mathematica is built to provide industrial-strength capabilities—with robust, efficient algorithms across all areas, capable of handling large-scale problems, with parallelism, GPU computing …
Mathematics | Definition, History, & Importance | Britannica
Apr 30, 2025 · mathematics, the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with …
Wolfram MathWorld: The Web's Most Extensive Mathematics …
May 22, 2025 · Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.
Wolfram|Alpha: Computational Intelligence
Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, …
MATHEMATICAL Definition & Meaning - Merriam-Webster
The meaning of MATHEMATICAL is of, relating to, or according with mathematics. How to use mathematical in a sentence.
Mathematics - Encyclopedia of Mathematics
Mar 30, 2012 · In the 17th century new questions in natural science and technology compelled mathematicians to concentrate their attention on the creation of methods to allow the …
MATHEMATICAL | English meaning - Cambridge Dictionary
mathematical formula The researchers used a mathematical formula to calculate the total population number. mathematical problem It was a mathematical problem that he could not …
Mathematical - definition of mathematical by The Free Dictionary
mathematical - of or pertaining to or of the nature of mathematics; "a mathematical textbook"; "slide rules and other mathematical instruments"; "a mathematical solution to a problem"; …
What is Mathematics? – Mathematical Association of America
Math is about getting the right answers, and we want kids to learn to think so they get the right answer. My reaction was visceral and immediate. “This is wrong. The emphasis needs to be on …
Mathematics - Wikipedia
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
Wolfram Mathematica: Modern Technical Computing
Mathematica is built to provide industrial-strength capabilities—with robust, efficient algorithms across all areas, capable of handling large-scale problems, with parallelism, GPU computing …
Mathematics | Definition, History, & Importance | Britannica
Apr 30, 2025 · mathematics, the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with …
Wolfram MathWorld: The Web's Most Extensive Mathematics …
May 22, 2025 · Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.
Wolfram|Alpha: Computational Intelligence
Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, …
MATHEMATICAL Definition & Meaning - Merriam-Webster
The meaning of MATHEMATICAL is of, relating to, or according with mathematics. How to use mathematical in a sentence.
Mathematics - Encyclopedia of Mathematics
Mar 30, 2012 · In the 17th century new questions in natural science and technology compelled mathematicians to concentrate their attention on the creation of methods to allow the …
MATHEMATICAL | English meaning - Cambridge Dictionary
mathematical formula The researchers used a mathematical formula to calculate the total population number. mathematical problem It was a mathematical problem that he could not …
Mathematical - definition of mathematical by The Free Dictionary
mathematical - of or pertaining to or of the nature of mathematics; "a mathematical textbook"; "slide rules and other mathematical instruments"; "a mathematical solution to a problem"; …
What is Mathematics? – Mathematical Association of America
Math is about getting the right answers, and we want kids to learn to think so they get the right answer. My reaction was visceral and immediate. “This is wrong. The emphasis needs to be …
