© 2010

Theoretical Statistics

Topics for a Core Course

  • Comprehensive coverage of estimation and hypothesis testing, frequentist and Bayesian paradigms, large and small sample methods, and the theory underlying numerical algorithms

  • Detailed and rigorous exposition designed to make the material clear and accessible

  • Rich collection of exercises, many with solutions, pushing students to learn the material well enough to use it in their own research and helping them appreciate its relevance to diverse applications


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


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.


Estimator Likelihood decision theory estimation hypothesis testing large sample theory

Authors and affiliations

  1. 1.Dept. StatisticsUniversity of MichiganAnn ArborUSA

About the authors

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

Bibliographic information

  • Book Title Theoretical Statistics
  • Book Subtitle Topics for a Core Course
  • Authors Robert W. Keener
  • Series Title Springer Texts in Statistics
  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-93838-7
  • Softcover ISBN 978-1-4614-2670-7
  • eBook ISBN 978-0-387-93839-4
  • Series ISSN 1431-875X
  • Edition Number 1
  • Number of Pages XVIII, 538
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Statistical Theory and Methods
  • Buy this book on publisher's site
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From the reviews:

“The book is innovative in the presentation and in mashing the traditional material with modern topics. The presentation shows a great mastery of the subject. … recommended to someone who has a working knowledge of statistics and would like to learn more about the theory. … As a text for a course, the book is versatile. … The mathematical level is correct for a first year graduate course and may be appropriate at some universities for courses whose primary audience is seniors.” (Stephan Morgenthaler, Mathematical Reviews, Issue 2011 m)

“This volume provides an excellent course in the mathematical theory underlying statistical ideas and methods, for advanced … students. The amount of material covered is indicated by the fact that it evolved from a three-semester sequence of courses given by the author. Its suitability as a course text is materially aided by very extensive exercises, along with solutions to selected exercises. Anyone who works through this book will end up with a first class understanding of the mathematical ideas underlying modern statistical concepts and methods.” (David J. Hand, International Statistical Review, Vol. 80 (1), 2012)

“The book extensively covers classic and modern topics of theoretical statistics in a rigorous manner. … The book provides more than 400 exercise problems. … There are many books on statistical theory but very few have such great breadth and scope of materials as this book. … the book is well written and it is a great addition to the collection of books on statistical theory. … It will serve well both as a textbook and a reference book.” (Xianggui Qu, Technometrics, Vol. 53 (3), August, 2011)