Large Sample Techniques for Statistics

✍ Scribed by Jiming Jiang (auth.)

• Publisher: Springer-Verlag New York
• Year: 2010
• Tongue: English
• Leaves: 628
• Series: Springer Texts in Statistics 0
• Edition: 1
• Category: Library

✦ Synopsis

This book offers a comprehensive guide to large sample techniques in statistics. More importantly, it focuses on thinking skills rather than just what formulae to use; it provides motivations, and intuition, rather than detailed proofs; it begins with very simple techniques, and connects theory and applications in entertaining 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 10 chapters contains at least one section of case study. The last five chapters are devoted to special areas of applications. The sections of case studies and chapters of applications fully demonstrate how to use methods developed from large sample theory in various, less-than-textbook situations. The book is supplemented by a large number of exercises, giving the readers plenty of opportunities to practice what they have learned. The book is mostly self-contained with the appendices providing some backgrounds for matrix algebra and mathematical statistics. The book is intended for a wide audience, ranging from senior undergraduate students to researchers with Ph.D. degrees. A first course in mathematical statistics and a course in calculus are prerequisites. Jiming Jiang is a Professor of Statistics at the University of California, Davis. He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. He is the author of another Springer book, Linear and Generalized Linear Mixed Models and Their Applications (2007). Jiming Jiang is a prominent researcher in the fields of mixed effects models, small area estimation and model selection. Most of his research papers have involved large sample techniques. He is currently an Associate Editor of the Annals of Statistics.

✦ Table of Contents

Front Matter....Pages 1-17
The ε - δ Arguments....Pages 1-18
Modes of Convergence....Pages 19-49
Big O , Small o , and the Unspecified c ....Pages 51-79
Asymptotic Expansions....Pages 81-126
Inequalities....Pages 127-171
Sums of Independent Random Variables....Pages 173-213
Empirical Processes....Pages 215-238
Martingales....Pages 239-281
Time and Spatial Series....Pages 283-315
Stochastic Processes....Pages 317-355
Nonparametric Statistics....Pages 357-391
Mixed Effects Models....Pages 393-431
Small-Area Estimation....Pages 433-470
Jackknife and Bootstrap....Pages 471-521
Markov-Chain Monte Carlo....Pages 523-551
Back Matter....Pages 553-609

✦ Subjects

Statistical Theory and Methods