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When I took courses in theoretical statistics as an undergrad 10 years ago, we used Modern Mathematical Statistics by Dudewicz and Mishra. I find myself referring back to the book now and am reminded some of the code examples are in assembly for an IBM 370. While quaint, I cannot help but feel this is somewhat dated.

What high quality books exist of more recent vintage?

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  • $\begingroup$ Size (pages ~ nr. theorems) and year published would be useful too. $\endgroup$
    – denis
    Jun 27, 2011 at 10:18
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    $\begingroup$ All contributions are warmly welcome, but those without any explanation will be deleted. $\endgroup$
    – whuber ♦
    Dec 19, 2011 at 14:51

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I've been studying in Mathematical Statistics by Jun Shao this summer. It certainly takes a theoretical approach. The exposition is extremely clear and there are tons of exercises.

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    $\begingroup$ and you can get the exercises and solutions book too: books.google.ca/… $\endgroup$
    – PeterR
    Jun 27, 2011 at 11:32
  • $\begingroup$ What's the meaning of "mathematical statistics", isn't statistics already a topic of maths? Whenever I think "statistics", I think "mathematics"at the same time. $\endgroup$
    – Red Banana
    Jul 4, 2012 at 23:55
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A bit late, but anyway...

"Theoretical Statistics"
Keener, Robert W.
1st Edition., 2010, XVII, 538 p.
Hardcover, ISBN 978-0-387-93838-7

About the 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.

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Casella and Berger's Statistical Inference is theory-heavy, and it's the standard text for a first graduate course in statistics.

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  • $\begingroup$ I think this text is often general at the expense of readability. I also think many of the exercises are difficult to comprehend what the answer should be. There is a solution manual but it has it's problems also. $\endgroup$
    – user9352
    Apr 20, 2012 at 2:52
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It depends on what kind of statistics book you want to learn. Mathematical statistics and data analysis written by John A. Rice is recommended if you want to learn some fundamental knowledge of statistics. Basically it talks about frequentist statistics. Besides, Bayesian concept is also an important theory in statistics. Bayesian data analysis written by Andrew Gelman is an advanced book for you.

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