A Course In Mathematical Statistics And Large Sample Theory

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A Course in Mathematical Statistics and Large Sample Theory

Rabi Bhattacharya,Lizhen Lin,Victor Patrangenaru
A Course in Mathematical Statistics and Large Sample Theory Book PDF

Author : Rabi Bhattacharya,Lizhen Lin,Victor Patrangenaru
Publisher : Springer
Page : 389 pages
File Size : 40,9 Mb
Release : 2016-08-13
Category : Mathematics
ISBN : 9781493940325

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A Course in Mathematical Statistics and Large Sample Theory by Rabi Bhattacharya,Lizhen Lin,Victor Patrangenaru Pdf

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.

A Course in Large Sample Theory

Thomas S. Ferguson
A Course in Large Sample Theory Book PDF

Author : Thomas S. Ferguson
Publisher : Routledge
Page : 256 pages
File Size : 52,8 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9781351470063

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A Course in Large Sample Theory by Thomas S. Ferguson Pdf

A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.

Large Sample Techniques for Statistics

Jiming Jiang
Large Sample Techniques for Statistics Book PDF

Author : Jiming Jiang
Publisher : Springer Nature
Page : 689 pages
File Size : 53,7 Mb
Release : 2022-04-04
Category : Mathematics
ISBN : 9783030916954

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Large Sample Techniques for Statistics by Jiming Jiang Pdf

This book offers a comprehensive guide to large sample techniques in statistics. With a focus on developing analytical skills and understanding motivation, Large Sample Techniques for Statistics begins with fundamental techniques, and connects theory and applications in engaging ways. The first five chapters review some of the basic techniques, such as the fundamental epsilon-delta arguments, Taylor expansion, different types of convergence, and inequalities. The next five chapters discuss limit theorems in specific situations of observational data. Each of the first ten chapters contains at least one section of case study. The last six chapters are devoted to special areas of applications. This new edition introduces a final chapter dedicated to random matrix theory, as well as expanded treatment of inequalities and mixed effects models. The book's case studies and applications-oriented chapters demonstrate how to use methods developed from large sample theory in real world situations. The book is supplemented by a large number of exercises, giving readers opportunity to practice what they have learned. Appendices provide context for matrix algebra and mathematical statistics. The Second Edition seeks to address new challenges in data science. This text is intended for a wide audience, ranging from senior undergraduate students to researchers with doctorates. A first course in mathematical statistics and a course in calculus are prerequisites..

Elements of Large-Sample Theory

E.L. Lehmann
Elements of Large Sample Theory Book PDF

Author : E.L. Lehmann
Publisher : Springer Science & Business Media
Page : 640 pages
File Size : 49,5 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387227290

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Elements of Large-Sample Theory by E.L. Lehmann Pdf

Written by one of the main figures in twentieth century statistics, this book provides a unified treatment of first-order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level making it accessible to most readers.

A First Course Mathematical Statistics

C. E. Weatherburn
A First Course Mathematical Statistics Book PDF

Author : C. E. Weatherburn
Publisher : CUP Archive
Page : 302 pages
File Size : 44,6 Mb
Release : 1949-01-02
Category : Mathematics
ISBN : 0521091586

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A First Course Mathematical Statistics by C. E. Weatherburn Pdf

This book provides the mathematical foundations of statistics. Its aim is to explain the principles, to prove the formulae to give validity to the methods employed in the interpretation of statistical data. Many examples are included but, since the primary emphasis is on the underlying theory, it is of interest to students of a wide variety of subjects: biology, psychology, agriculture, economics, physics, chemistry, and (of course) mathematics.

All of Statistics

Larry Wasserman
All of Statistics Book PDF

Author : Larry Wasserman
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 40,9 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9780387217369

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All of Statistics by Larry Wasserman Pdf

Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.

A Course in the Large Sample Theory of Statistical Inference

W. Jackson Hall,David Oakes
A Course in the Large Sample Theory of Statistical Inference Book PDF

Author : W. Jackson Hall,David Oakes
Publisher : CRC Press
Page : 321 pages
File Size : 40,6 Mb
Release : 2023-12-14
Category : Mathematics
ISBN : 9781498726085

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A Course in the Large Sample Theory of Statistical Inference by W. Jackson Hall,David Oakes Pdf

Provides accessible introduction to large sample theory with moving alternatives Elucidates mathematical concepts using simple practical examples Includes problem sets and solutions for each chapter Uses the moving alternative formulation developed by LeCam but requires a minimum of mathematical prerequisites

Examples and Problems in Mathematical Statistics

Shelemyahu Zacks
Examples and Problems in Mathematical Statistics Book PDF

Author : Shelemyahu Zacks
Publisher : John Wiley & Sons
Page : 499 pages
File Size : 43,8 Mb
Release : 2013-12-17
Category : Mathematics
ISBN : 9781118605837

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Examples and Problems in Mathematical Statistics by Shelemyahu Zacks Pdf

Provides the necessary skills to solve problems in mathematical statistics through theory, concrete examples, and exercises With a clear and detailed approach to the fundamentals of statistical theory, Examples and Problems in Mathematical Statistics uniquely bridges the gap between theory andapplication and presents numerous problem-solving examples that illustrate the relatednotations and proven results. Written by an established authority in probability and mathematical statistics, each chapter begins with a theoretical presentation to introduce both the topic and the important results in an effort to aid in overall comprehension. Examples are then provided, followed by problems, and finally, solutions to some of the earlier problems. In addition, Examples and Problems in Mathematical Statistics features: Over 160 practical and interesting real-world examples from a variety of fields including engineering, mathematics, and statistics to help readers become proficient in theoretical problem solving More than 430 unique exercises with select solutions Key statistical inference topics, such as probability theory, statistical distributions, sufficient statistics, information in samples, testing statistical hypotheses, statistical estimation, confidence and tolerance intervals, large sample theory, and Bayesian analysis Recommended for graduate-level courses in probability and statistical inference, Examples and Problems in Mathematical Statistics is also an ideal reference for applied statisticians and researchers.

A Course in the Large Sample Theory of Statistical Inference

William Jackson Hall,David Oakes (Statistician)
A Course in the Large Sample Theory of Statistical Inference Book PDF

Author : William Jackson Hall,David Oakes (Statistician)
Publisher : Unknown
Page : 0 pages
File Size : 48,6 Mb
Release : 2023-12
Category : Statistical hypothesis testing
ISBN : 0429160089

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A Course in the Large Sample Theory of Statistical Inference by William Jackson Hall,David Oakes (Statistician) Pdf

"This book provides an accessible but rigorous introduction to asymptotic theory in parametric statistical models. Asymptotic results for estimation and testing are derived using the "moving alternative" formulation due to R. A. Fisher and L. Le Cam. Later chapters include discussions of linear rank statistics and of chi-squared tests for contingency table analysis, including situations where parameters are estimated from the complete ungrouped data. The book is based on lecture notes prepared by the first author, subsequently edited, expanded and updated by the second author. Some facility with linear algebra and with real analysis including "epsilon-delta" arguments is required. Concepts and results from measure theory are explained when used. Familiarity with undergraduate probability and statistics including basic concepts of estimation and hypothesis testing is necessary, and experience with applying these concepts to data analysis would be very helpful"--

Probability and Statistical Theory for Applied Researchers

T W Epps
Probability and Statistical Theory for Applied Researchers Book PDF

Author : T W Epps
Publisher : World Scientific Publishing Company
Page : 828 pages
File Size : 42,8 Mb
Release : 2013-08-16
Category : Mathematics
ISBN : 9789814513173

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Probability and Statistical Theory for Applied Researchers by T W Epps Pdf

This book presents the theory of probability and mathematical statistics at a level suitable for researchers at the frontiers of applied disciplines. Examples and exercises make essential concepts in measure theory and analysis accessible to those with preparation limited to vector calculus. Complete, detailed solutions to all the exercises demonstrate techniques of problem solving and provide immediate feedback. Part I, The Theory of Probability, starts with elementary set theory and proceeds through basic measure and probability, random variables, integration and mathematical expectation. It concludes with an extensive survey of models for distributions of random variables. Part II, The Theory of Statistics, begins with sampling theory and distribution theory for statistics from normal populations, proceeds to asymptotic (large-sample) theory, and on to point and interval estimation and tests of parametric hypotheses. The last three chapters cover tests of nonparametric hypotheses, Bayesian methods, and linear and nonlinear regression. Researchers and graduate students in applied fields such as actuarial science, biostatistics, economics, finance, mathematical psychology, and systems engineering will find this book to be a valuable learning tool and an essential reference. Sample Chapter(s) Chapter 1: Probability on Abstract Sets (476 KB) Chapter 5: Sampling Distributions (405 KB) Request Inspection Copy

A Course in Large Sample Theory

Thomas S. Ferguson
A Course in Large Sample Theory Book PDF

Author : Thomas S. Ferguson
Publisher : Routledge
Page : 140 pages
File Size : 46,6 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9781351470056

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A Course in Large Sample Theory by Thomas S. Ferguson Pdf

A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.

Large Sample Methods in Statistics (1994)

Pranab K. Sen,Julio M. Singer
Large Sample Methods in Statistics 1994 Book PDF

Author : Pranab K. Sen,Julio M. Singer
Publisher : CRC Press
Page : 394 pages
File Size : 44,9 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351361163

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Large Sample Methods in Statistics (1994) by Pranab K. Sen,Julio M. Singer Pdf

This text bridges the gap between sound theoretcial developments and practical, fruitful methodology by providing solid justification for standard symptotic statistical methods. It contains a unified survey of standard large sample theory and provides access to more complex statistical models that arise in diverse practical applications.

Large Sample Techniques for Statistics

Jiming Jiang
Large Sample Techniques for Statistics Book PDF

Author : Jiming Jiang
Publisher : Springer Science & Business Media
Page : 612 pages
File Size : 45,8 Mb
Release : 2010-06-30
Category : Mathematics
ISBN : 9781441968272

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Large Sample Techniques for Statistics by Jiming Jiang Pdf

In a way, the world is made up of approximations, and surely there is no exception in the world of statistics. In fact, approximations, especially large sample approximations, are very important parts of both theoretical and - plied statistics.TheGaussiandistribution,alsoknownasthe normaldistri- tion,is merelyonesuchexample,dueto thewell-knowncentrallimittheorem. Large-sample techniques provide solutions to many practical problems; they simplify our solutions to di?cult, sometimes intractable problems; they j- tify our solutions; and they guide us to directions of improvements. On the other hand, just because large-sample approximations are used everywhere, and every day, it does not guarantee that they are used properly, and, when the techniques are misused, there may be serious consequences. 2 Example 1 (Asymptotic? distribution). Likelihood ratio test (LRT) is one of the fundamental techniques in statistics. It is well known that, in the 2 “standard” situation, the asymptotic null distribution of the LRT is?,with the degreesoffreedomequaltothe di?erencebetweenthedimensions,de?ned as the numbers of free parameters, of the two nested models being compared (e.g., Rice 1995, pp. 310). This might lead to a wrong impression that the 2 asymptotic (null) distribution of the LRT is always? . A similar mistake 2 might take place when dealing with Pearson’s? -test—the asymptotic distri- 2 2 bution of Pearson’s? -test is not always? (e.g., Moore 1978).

Theory of Statistics

Mark J. Schervish
Theory of Statistics Book PDF

Author : Mark J. Schervish
Publisher : Springer Science & Business Media
Page : 732 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242505

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Theory of Statistics by Mark J. Schervish Pdf

The aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D. An important strength of this book is that it provides a mathematically rigorous and even-handed account of both Classical and Bayesian inference in order to give readers a broad perspective. For example, the "uniformly most powerful" approach to testing is contrasted with available decision-theoretic approaches.

Theoretical Statistics

Robert W. Keener
Theoretical Statistics Book PDF

Author : Robert W. Keener
Publisher : Springer Science & Business Media
Page : 538 pages
File Size : 47,9 Mb
Release : 2010-09-08
Category : Mathematics
ISBN : 9780387938394

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Theoretical Statistics by Robert W. Keener Pdf

Intended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis and topology. Measure theory is used, but the notation and basic results needed are presented in an initial chapter on probability, so prior knowledge of these topics is not essential. The presentation is designed to expose students to as many of the central ideas and topics in the discipline as possible, balancing various approaches to inference as well as exact, numerical, and large sample methods. Moving beyond more standard material, the book includes chapters introducing bootstrap methods, nonparametric regression, equivariant estimation, empirical Bayes, and sequential design and analysis. The book has a rich collection of exercises. Several of them illustrate how the theory developed in the book may be used in various applications. Solutions to many of the exercises are included in an appendix.