Theoretical Statistics
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Theoretical Statistics
Author: Robert W. Keener
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-09-08
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.
Theoretical Statistics
A text that stresses the general concepts of the theory of statistics Theoretical Statistics provides a systematic statement of the theory of statistics, emphasizing general concepts rather than mathematical rigor. Chapters 1 through 3 provide an overview of statistics and discuss some of the basic philosophical ideas and problems behind statistica
Theory of Statistics
Author: Mark J. Schervish
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D. An important strength of this book is that it provides a mathematically rigorous and even-handed account of both Classical and Bayesian inference in order to give readers a broad perspective. For example, the "uniformly most powerful" approach to testing is contrasted with available decision-theoretic approaches.