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Large Sample Techniques for Statistics

  • Jiming Jiang

Part of the Springer Texts in Statistics book series (STS, volume 0)

Table of contents

  1. Front Matter
    Pages 1-17
  2. Jiming Jiang
    Pages 1-18
  3. Jiming Jiang
    Pages 19-49
  4. Jiming Jiang
    Pages 51-79
  5. Jiming Jiang
    Pages 81-126
  6. Jiming Jiang
    Pages 127-171
  7. Jiming Jiang
    Pages 173-213
  8. Jiming Jiang
    Pages 215-238
  9. Jiming Jiang
    Pages 239-281
  10. Jiming Jiang
    Pages 283-315
  11. Jiming Jiang
    Pages 317-355
  12. Jiming Jiang
    Pages 357-391
  13. Jiming Jiang
    Pages 393-431
  14. Jiming Jiang
    Pages 433-470
  15. Jiming Jiang
    Pages 471-521
  16. Jiming Jiang
    Pages 523-551
  17. Back Matter
    Pages 553-609

About this book

Introduction

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.

Keywords

Approximations Asymptotic Theory Large Sample Theory Limit Theorems Parametric statistics Random variable Statistical Applications mathematical statistics

Authors and affiliations

  • Jiming Jiang
    • 1
  1. 1.Dept. StatisticsUniversity of CaliforniaDavisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-6827-2
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-6826-5
  • Online ISBN 978-1-4419-6827-2
  • Series Print ISSN 1431-875X
  • Buy this book on publisher's site