9780521102827

Comparison of Statistical Experiments

by
  • ISBN13:

    9780521102827

  • ISBN10:

    0521102820

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2009-03-12
  • Publisher: Cambridge University Press
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  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

Summary

There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, ordering, equivalence, completeness and convergence are explored. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians.

Table of Contents

Preface
Acknowledgements
Statistical experiments within the measure theoretical framework
Convexity
Two-person, zero-sum games
Statistical decision problems
Vector lattices
Deficiencies
Equivalence, representations and functionals of experiments
Comparison of linear models
Majorisation and approximate majorisation
Complements: Further examples, problems and comments
List of symbols
Author index
Additional references
Subject index
Table of Contents provided by Publisher. All Rights Reserved.

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