Mathematical statistics
New York
9780387938394
0387938397
2017-01-18
Theoretical statistics.
Print version:
Electronic books
2010
en
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.
676700036
676700036
Theoretical statistics : topics for a core course
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.
2010
Keener
Robert W.
Robert W. Keener
Springer texts in statistics
Springer texts in statistics.
Springer
Probability
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