Essentials of Statistical Inference,9780521839716

Essentials of Statistical Inference

by
ISBN13: 9780521839716
ISBN10: 0521839718
Format: Hardcover
Pub. Date: 2005-07-25
Publisher(s): Cambridge University Press
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Summary

This series of high-quality upper-division textbooks and expository monographs covers all aspects of stochastic applicable mathematics. The topics range from pure and applied statistics to probability theory, operations research, optimization, and mathematical programming. The books contain clear presentations of new developments in the field and also of the state of the art in classical methods. While emphasizing rigorous treatment of theoretical methods, the books also contain applications and discussions of new techniques made possible by advances in computational practice. Book jacket.

Table of Contents

Preface ix
Introduction
1(3)
Decision theory
4(18)
Formulation
4(1)
The risk function
5(2)
Criteria for a good decision rule
7(4)
Randomised decision rules
11(1)
Finite decision problems
11(7)
Finding minimax rules in general
18(1)
Admissibility of Bayes rules
19(1)
Problems
19(3)
Bayesian methods
22(43)
Fundamental elements
22(6)
The general form of Bayes rules
28(4)
Back to minimax...
32(1)
Shrinkage and the James--Stein estimator
33(5)
Empirical Bayes
38(1)
Choice of prior distributions
39(3)
Computational techniques
42(6)
Hierarchical modelling
48(4)
Predictive distributions
52(3)
Data example: Coal-mining disasters
55(2)
Data example: Gene expression data
57(3)
Problems
60(5)
Hypothesis testing
65(16)
Formulation of the hypothesis testing problem
65(3)
The Neyman--Pearson Theorem
68(1)
Uniformly most powerful tests
69(4)
Bayes factors
73(5)
Problems
78(3)
Special models
81(9)
Exponential families
81(5)
Transformation families
86(2)
Problems
88(2)
Sufficiency and completeness
90(8)
Definitions and elementary properties
90(4)
Completeness
94(1)
The Lehmann--Scheffe Theorem
95(1)
Estimation with convex loss functions
95(1)
Problems
96(2)
Two-sided tests and conditional inference
98(22)
Two-sided hypotheses and two-sided tests
99(6)
Conditional inference, ancillarity and similar tests
105(9)
Confidence sets
114(3)
Problems
117(3)
Likelihood theory
120(20)
Definitions and basic properties
120(5)
The Cramer--Rao Lower Bound
125(2)
Convergence of sequences of random variables
127(1)
Asymptotic properties of maximum likelihood estimators
128(4)
Likelihood ratio tests and Wilks' Theorem
132(2)
More on multiparameter problems
134(3)
Problems
137(3)
Higher-order theory
140(29)
Preliminaries
141(2)
Parameter orthogonality
143(2)
Pseudo-likelihoods
145(1)
Parametrisation invariance
146(2)
Edgeworth expansion
148(1)
Saddlepoint expansion
149(3)
Laplace approximation of integrals
152(1)
The p* formula
153(6)
Conditional inference in exponential families
159(1)
Bartlett correction
160(1)
Modified profile likelihood
161(2)
Bayesian asymptotics
163(1)
Problems
164(5)
Predictive inference
169(21)
Exact methods
169(3)
Decision theory approaches
172(3)
Methods based on predictive likelihood
175(4)
Asymptotic methods
179(4)
Bootstrap methods
183(2)
Conclusions and recommendations
185(1)
Problems
186(4)
Bootstrap methods
190(28)
An inference problem
191(3)
The prepivoting perspective
194(7)
Data example: Bioequivalence
201(2)
Further numerical illustrations
203(5)
Conditional inference and the bootstrap
208(6)
Problems
214(4)
Bibliography 218(5)
Index 223

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