Large Sample Techniques for Statistics

by Jiming Jiang

Overview

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..

Product Details

ISBN-13:	9783030916978
Publisher:	Springer International Publishing
Publication date:	04/05/2022
Series:	Springer Texts in Statistics
Edition description:	Second Edition 2022
Pages:	685
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Jiming Jiang is Professor of Statistics and a former Director of Statistical Laboratory at the University of California, Davis. He is a prominent researcher in the fields of mixed effects models, small area estimation, model selection, and statistical genetics. He is the author of Linear and Generalized Linear Mixed Models and Their Applications, 2nd Edition (Springer 2021), Robust Mixed Model Analysis (2019), Asymptotic Analysis of Mixed Effects Models: Theory, Applications, and Open Problems (2017), and The Fence Methods (with T. Ngyuen, 2016). Jiming Jiang has been editorial board member of The Annals of Statistics and Journal of the American Statistical Association, among others. He is a Fellow of the American Association for the Advancement of Science, the American Statistical Association, and the Institute of Mathematical Statistics; an elected member of the International Statistical Institute; and a Yangtze River Scholar (Chaired Professor, 2017-2020).

Table of Contents

Chapter 1. The -δ Arguments.- Chapter 2. Modes of Convergence.- Chapter 3. Big O, Small o, and the Unspecified c.- Chapter 4. Asymptotic Expansions.- Chapter 5. Inequalities.- Chapter 6. Sums of Independent Random Variables.- Chapter 7. Empirical Processes.- Chapter 8. Martingales.- Chapter 9. Time and Spatial Series.- Chapter 10. Shastic Processes.- Chapter 11. Nonparametric Statistics.- Chapter 12. Mixed Effects Models.- Chapter 13. Small-Area Estimation.- Chapter 14. Jackknife and Bootstrap.- Chapter 15. Markov-Chain Monte Carlo.- Chapter 16. Random Matrix Theory.

Editorial Reviews

From the reviews:

“Each chapter is supplemented by a series of exercises. … The book clearly helps the beginner to learn the foundations and techniques of large sample theory in statistics in part one, provides an outline of more advanced tools in part two and gives an impressions of the flavor of their applicability in part three. It is very suitable as a survey of and a guide to the addressed topics … .” (Erich Haeusler, Mathematical Reviews, Issue 2011 k)

“Jiming Jiang’s book on large sample techniques is a very welcome addition to the literature. Its strong points include the breadth of covered material, choice of relevant and interesting topics, lucid and attractive style of presentation, and sound pedagogical aspects. … Along with its excellent coverage of the fundamentals in its initial chapters, the book addresses a number of important topics in the latter half as well. … All in all, Large Sample Techniques in Statistics is an excellent book that I recommend whole-heartedly.” (Moulinath Banerjee, Journal of the American Statistical Association, Vol. 106 (496), December, 2011)

“A book on techniques for large samples in statistics is timely. … Anyone with a background in … mathematical statistics can benefit from the very thorough nature of the book. The author is systematic and detailed in the developing of each topic and utilizes examples and cases to illustrate the practical import of each concept. … I found the book quite enlightening as the author again and again pointed out the confusions and misinterpretations that often arise in the context of common applications … .” (Mark A. McComb, Technometrics, Vol. 54 (1), February, 2012)

From the Publisher