Theoretical Statistics

Topics for a Core Course

  • Robert W.┬áKeener

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

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Robert W. Keener
    Pages 1-24
  3. Robert W. Keener
    Pages 25-38
  4. Robert W. Keener
    Pages 61-83
  5. Robert W. Keener
    Pages 85-99
  6. Robert W. Keener
    Pages 101-113
  7. Robert W. Keener
    Pages 115-127
  8. Robert W. Keener
    Pages 129-149
  9. Robert W. Keener
    Pages 151-194
  10. Robert W. Keener
    Pages 195-203
  11. Robert W. Keener
    Pages 205-218
  12. Robert W. Keener
    Pages 219-253
  13. Robert W. Keener
    Pages 255-267
  14. Robert W. Keener
    Pages 269-299
  15. Robert W. Keener
    Pages 301-318
  16. Robert W. Keener
    Pages 319-342
  17. Robert W. Keener
    Pages 343-366
  18. Robert W. Keener
    Pages 367-390
  19. Robert W. Keener
    Pages 391-403

About this book

Introduction

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. Robert Keener is Professor of Statistics at the University of Michigan and a fellow of the Institute of Mathematical Statistics.

Keywords

Estimator Likelihood decision theory estimation hypothesis testing large sample theory

Authors and affiliations

  • Robert W.┬áKeener
    • 1
  1. 1.Dept. StatisticsUniversity of MichiganAnn ArborUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-93839-4
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-93838-7
  • Online ISBN 978-0-387-93839-4
  • Series Print ISSN 1431-875X
  • About this book
Industry Sectors
Pharma
Biotechnology
Electronics
Telecommunications
Aerospace
Oil, Gas & Geosciences