Theoretical Statistics

Robert Keener - Collection Springer texts in statistics

538 pages, parution le 01/09/2010

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Résumé

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.

L'auteur - Robert Keener

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

Sommaire

Probability and measure
Exponential families
Risk, sufficiency, completeness, and ancillarity
Unbiased estimation
Curved exponential families
Conditional distributions
Bayesian estimation
Large sample theory
Estimating equations and maximum likelihood
Equivariant estimation
Empirical bayes and shrinkage estimators
Hypothesis testing
Optimal tests in higher dimensions
General linear model
Bayesian inference: Modeling and computation
Asymptotic optimality
Large sample theory for likelihood ratio tests
Nonparametric regression
Bootstrap methods
Sequential methods

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Robert Keener
Collection	Springer texts in statistics
Parution	01/09/2010
Nb. de pages	538
Couverture	Broché
Intérieur	Noir et Blanc
EAN13	9780387938387
ISBN13	978-0-387-93838-7