Essentials of Statistical Inference

ISBN-10: 0521548667

ISBN-13: 9780521548663

Edition: 2010

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Description: 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.

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Book details

Copyright year: 2010
Publisher: Cambridge University Press
Publication date: 3/29/2010
Binding: Paperback
Pages: 236
Size: 6.75" wide x 9.75" long x 0.75" tall
Weight: 1.144
Language: English

G. A. Young is Professor of Statistics at Imperial College London.

Preface
Introduction
Decision theory
Formulation
The risk function
Criteria for a good decision rule
Randomised decision rules
Finite decision problems
Finding minimax rules in general
Admissibility of Bayes rules
Problems
Bayesian methods
Fundamental elements
The general form of Bayes rules
Back to minimax…
Shrinkage and the James-Stein estimator
Empirical Bayes
Choice of prior distributions
Computational techniques
Hierarchical modeling
Predictive distributions
Data example: Coal-mining disasters
Data example: Gene expression data
Problems
Hypothesis testing
Formulation of the hypothesis testing problem
The Neyman-Pearson Theorem
Uniformly most powerful tests
Bayes factors
Problems
Special models
Exponential families
Transformation families
Problems
Sufficiency and completeness
Definitions and elementary properties
Completeness
The Lehmann-Scheff� Theorem
Estimation with convex loss functions
Problems
Two-sided tests and conditional inference
Two-sided hypotheses and two-sided tests
Conditional inference, ancillarity and similar tests
Confidence sets
Problems
Likelihood theory
Definitions and basic properties
The Cram�r-Rao Lower Bound
Convergence of sequences of random variables
Asymptotic properties of maximum likelihood estimators
Likelihood ratio tests and Wilks' Theorem
More on multiparameter problems
Problems
Higher-order theory
Preliminaries
Parameter orthogonality
Pseudo-likelihoods
Parametrisation invariance
Edgeworth expansion
Saddlepointexpansion
Laplace approximation of integrals
The p<sup>*</sup> formula
Conditional inference in exponential families
Bartlettcorrection
Modified profile likelihood
Bayesian asymptotics
Problems
Predictive inference
Exactmethods
Decision theory approaches
Methods based on predictive likelihood
Asymptotic methods
Bootstrap methods
Conclusions and recommendations
Problems
Bootstrap methods
An inference problem
The prepivoting perspective
Data example: Bioequivalence
Further numerical illustrations
Conditional inference and the bootstrap
Problems
Bibliography
Index
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