Essentials of Statistical Inference

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780521548663 | 0521548667
Cover: Paperback
Copyright: 3/29/2010

Rent

(Recommended)

$27.81

Term

Due

Price

Semester

Dec 12

$30.90

Quarter

Sep 1

$29.36

Short Term

Aug 13

$27.81

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping bag.
Buy Used

Usually Ships in 3-5 Business Days

$35.64
Buy New

Special Order: 1-2 Weeks

$49.45
eBook

Available Instantly

Online: 180 Days

Downloadable: 180 Days

*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.

$45.12*

This textbook presents the concepts and results underlying the Bayesian, frequentist, and Fisherian approaches to statistical inference, with particular emphasis on the contrasts between them. Aimed at advanced undergraduates and graduate students in mathematics and related disciplines, it covers basic mathematical theory as well as more advanced material, including such contemporary topics as Bayesian computation, higher-order likelihood theory, predictive inference, bootstrap methods, and conditional inference.

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

Please wait while the item is added to your bag...

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Essentials of Statistical Inference

Summary

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Essentials of Statistical Inference

Summary

Table of Contents

Supplemental Materials

Digital License