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Cambridge Series in Statistical and Probabilistic Mathematics : Essentials of Statistical Inference Series Number 16 - G. A. Young

Cambridge Series in Statistical and Probabilistic Mathematics

Essentials of Statistical Inference Series Number 16

Paperback

Published: 29th March 2010
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Aimed at advanced undergraduate and graduate students in mathematics and related disciplines, this book presents the concepts and results underlying the Bayesian, frequentist and Fisherian approaches, with particular emphasis on the contrasts between them. Computational ideas are explained, as well as basic mathematical theory. Written in a lucid and informal style, this concise text provides both basic material on the main approaches to inference, as well as more advanced material on developments in statistical theory, including: material on Bayesian computation, such as MCMC, higher-order likelihood theory, predictive inference, bootstrap methods and conditional inference. It contains numerous extended examples of the application of formal inference techniques to real data, as well as historical commentary on the development of the subject. Throughout, the text concentrates on concepts, rather than mathematical detail, while maintaining appropriate levels of formality. Each chapter ends with a set of accessible problems.

'This is a delightful book! It gives a well-written exposure to inference issues in statistics, very suitable for a first-year graduate course ... The authors present the material in a very good pedagogical manner. The examples are excellent, and the exercises are very instructive ... very much up to date and includes recent developments in the field.' MAA Reviews
'This is a solid book, ideal for advanced classes in the mathematical justification for statistical inference.' Journal of Recreational Mathematics
'I wish that I had had such a textbook during my student days ... this new book presents the core ideas of statistical inference in the unifying framework of decision theory and includes a fruitful discussion of the different foundational standpoints (Bayesian, Fisherian and frequentist) ... [it is] sufficiently precise to satisfy a mathematician and yet omitting too much technical detail that could hide the core of the ideas. Carefully selected examples from a rainbow of application areas such as baseball, coal-mining disasters or gene expression data make it even more enjoyable to read ... this book is a very nice graduate level textbook.' Journal of the Royal Statistical Society
'[This] book gives a clear and comprehensive account of the basic elements of statistical theory. It should make a good text for an advanced course on statistical inference ... Students will find it informative and challenging.' ISI Short Book Reviews
'Essentials of Statistical Inference is a book worth having.' Jane L. Harvill, Journal of the American Statistical Association
'The book is comprehensively written without dwelling in unnecessary details.' Iris Pigeot, Biometrics
'... gives a clear and comprehensive account of the basic elements of statistical theory ... a good text for an advanced course on statistical inference.' Publication of the International Statistical Institute
'The text presents the main concepts and results underlying different frameworks of inference, with particular emphasis on the contrasts among frequentist, Fisherian, and Bayesian approaches. It provides a depiction of basic material on these main approaches to inference, as well as more advanced material on recent developments in statistical theory, including higher-order likelihood inference, bootstrap methods, conditional inference, and predictive inference.' Zentralblatt MATH
"This is a delightful book! It gives a well-written exposure to inference issues in statistics, very suitable for a first-year graduate course...The authors present the material in a very good pedagogical manner. The examples are excellent, and the exercises are very instructive...very much up to date and includes recent developments in the field." MAA Reviews
"This is a solid book, ideal for advanced classes in the mathematical justification for statistical inference." Journal of Recreational Mathematics
"I wish that I had had such a textbook during my student days...this new book presents the core ideas of statistical inference in the unifying framework of decision theory and includes a fruitful discussion of the different foundational standpoints (Bayesian, Fisherian and frequentist)...[it is] sufficiently precise to satisfy a mathematician and yet omitting too much technical detail that could hide the core of the ideas. Carefully selected examples from a rainbow of application areas such as baseball, coal-mining disasters or gene expression data make it even more enjoyable to read...this book is a very nice graduate level textbook." Journal of the Royal Statistical Society
"[T]his book gives a clear and comprehensive account of the basic elements of statistical theory. It should make a good text for an advanced course on statistical inference...Students will find it informative and challenging." ISI Short Book Reviews
"Essentials of Statistical Inference is a book worth having." Jane L. Harvill, Baylor University for the Journal of The American Statistician
"The book is comprehensively written without dwelling in unnecessary details." Iris Pigeot, Biometrics
"This book is very unique in that the authors present the foundations of all three schools of inference and produce the essential theoretical results in each approach. This text also contains a great bibliography that is partially annotated. Readers should pay attention to the annotations as they are very enlightening. This book could easily be used for a modern first graduate level course in mathematical statistics." Michael R. Chernick, Significance

Prefacep. ix
Introductionp. 1
Decision theoryp. 4
Formulationp. 4
The risk functionp. 5
Criteria for a good decision rulep. 7
Randomised decision rulesp. 11
Finite decision problemsp. 11
Finding minimax rules in generalp. 18
Admissibility of Bayes rulesp. 19
Problemsp. 19
Bayesian methodsp. 22
Fundamental elementsp. 22
The general form of Bayes rulesp. 28
Back to minimax…p. 32
Shrinkage and the James-Stein estimatorp. 33
Empirical Bayesp. 38
Choice of prior distributionsp. 39
Computational techniquesp. 42
Hierarchical modelingp. 48
Predictive distributionsp. 52
Data example: Coal-mining disastersp. 55
Data example: Gene expression datap. 57
Problemsp. 60
Hypothesis testingp. 65
Formulation of the hypothesis testing problemp. 65
The Neyman-Pearson Theoremp. 68
Uniformly most powerful testsp. 69
Bayes factorsp. 73
Problemsp. 78
Special modelsp. 81
Exponential familiesp. 81
Transformation familiesp. 86
Problemsp. 88
Sufficiency and completenessp. 90
Definitions and elementary propertiesp. 90
Completenessp. 94
The Lehmann-Scheffé Theoremp. 95
Estimation with convex loss functionsp. 95
Problemsp. 96
Two-sided tests and conditional inferencep. 98
Two-sided hypotheses and two-sided testsp. 99
Conditional inference, ancillarity and similar testsp. 105
Confidence setsp. 114
Problemsp. 117
Likelihood theoryp. 120
Definitions and basic propertiesp. 120
The Cramér-Rao Lower Boundp. 125
Convergence of sequences of random variablesp. 127
Asymptotic properties of maximum likelihood estimatorsp. 128
Likelihood ratio tests and Wilks' Theoremp. 132
More on multiparameter problemsp. 134
Problemsp. 137
Higher-order theoryp. 140
Preliminariesp. 141
Parameter orthogonalityp. 143
Pseudo-likelihoodsp. 145
Parametrisation invariancep. 146
Edgeworth expansionp. 148
Saddlepointexpansionp. 149
Laplace approximation of integralsp. 152
The p* formulap. 153
Conditional inference in exponential familiesp. 159
Bartlettcorrectionp. 160
Modified profile likelihoodp. 161
Bayesian asymptoticsp. 163
Problemsp. 164
Predictive inferencep. 169
Exactmethodsp. 169
Decision theory approachesp. 172
Methods based on predictive likelihoodp. 175
Asymptotic methodsp. 179
Bootstrap methodsp. 183
Conclusions and recommendationsp. 185
Problemsp. 186
Bootstrap methodsp. 190
An inference problemp. 191
The prepivoting perspectivep. 194
Data example: Bioequivalencep. 201
Further numerical illustrationsp. 203
Conditional inference and the bootstrapp. 208
Problemsp. 214
Bibliographyp. 218
Indexp. 223
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780521548663
ISBN-10: 0521548667
Series: Cambridge Series in Statistical and Probabilistic Mathematics
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 236
Published: 29th March 2010
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.77 x 17.15  x 1.91
Weight (kg): 0.43