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Principles of Statistical Inference

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ISBN-10: 0521685672

ISBN-13: 9780521685672

Edition: 2006

Authors: D. R. Cox

List price: $44.99
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Description:

In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated…    
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Book details

List price: $44.99
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 8/10/2006
Binding: Paperback
Pages: 236
Size: 6.25" wide x 9.25" long x 0.50" tall
Weight: 0.836
Language: English

List of examples
Preface
Preliminaries
Summary
Starting point
Role of formal theory of inference
Some simple models
Formulation of objectives
Two broad approaches to statistical inference
Some further discussion
Parameters
Some concepts and simple applications
Summary
Likelihood
Sufficiency
Exponential family
Choice of priors for exponential family problems
Simple frequentist discussion
Pivots
Significance tests
Summary
General remarks
Simple significance test
One- and two-sided tests
Relation with acceptance and rejection
Formulation of alternatives and test statistics
Relation with interval estimation
Interpretation of significance tests
Bayesian testing
More complicated situations
Summary
General remarks
General Bayesian formulation
Frequentist analysis
Some more general frequentist developments
Some further Bayesian examples
Interpretations of uncertainty
Summary
General remarks
Broad roles of probability
Frequentist interpretation of upper limits
Neyman-Pearson operational criteria
Some general aspects of the frequentist approach
Yet more on the frequentist approach
Personalistic probability
Impersonal degree of belief
Reference priors
Temporal coherency
Degree of belief and frequency
Statistical implementation of Bayesian analysis
Model uncertainty
Consistency of data and prior
Relevance of frequentist assessment
Sequential stopping
A simple classification problem
Asymptotic theory
Summary
General remarks
Scalar parameter
Multidimensional parameter
Nuisance parameters
Tests and model reduction
Comparative discussion
Profile likelihood as an information summarizer
Constrained estimation
Semi-asymptotic arguments
Numerical-analytic aspects
Higher-order asymptotics
Further aspects of maximum likelihood
Summary
Multimodal likelihoods
Irregular form
Singular information matrix
Failure of model
Unusual parameter space
Modified likelihoods
Additional objectives
Summary
Prediction
Decision analysis
Point estimation
Non-likelihood-based methods
Randomization-based analysis
Summary
General remarks
Sampling a finite population
Design of experiments
A brief history
A personal view
References
Author index
Subject index