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Theory of Statistical Experiments

  • Book
  • © 1982

Overview

Authors:
  1. H. Heyer

    1. Mathematisches Institut, Universität Tübingen, Tübingen 1, West Germany

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Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
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  2. Games and Statistical Decisions

    • H. Heyer
    Pages 1-24

  3. Sufficient σ-Algebras and Statistics

    • H. Heyer
    Pages 25-41

  4. Sufficiency under Additional Assumptions

    • H. Heyer
    Pages 42-60

  5. Testing Experiments

    • H. Heyer
    Pages 61-82

  6. Testing Experiments Admitting an Isotone Likelihood Quotient

    • H. Heyer
    Pages 83-114

  7. Estimation Experiments

    • H. Heyer
    Pages 115-141

  8. Information and Sufficiency

    • H. Heyer
    Pages 142-173

  9. Invariance and the Comparison of Experiments

    • H. Heyer
    Pages 174-188

  10. Comparison of Finite Experiments

    • H. Heyer
    Pages 189-227

  11. Comparison with Extremely Informative Experiments

    • H. Heyer
    Pages 228-255

  12. Back Matter

    Pages 256-289
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Keywords

About this book

By a statistical experiment we mean the procedure of drawing a sample with the intention of making a decision. The sample values are to be regarded as the values of a random variable defined on some meas­ urable space, and the decisions made are to be functions of this random variable. Although the roots of this notion of statistical experiment extend back nearly two hundred years, the formal treatment, which involves a description of the possible decision procedures and a conscious attempt to control errors, is of much more recent origin. Building upon the work of R. A. Fisher, J. Neyman and E. S. Pearson formalized many deci­ sion problems associated with the testing of hypotheses. Later A. Wald gave the first completely general formulation of the problem of statisti­ cal experimentation and the associated decision theory. These achieve­ ments rested upon the fortunate fact that the foundations of probability had by then been laid bare, for it appears to be necessary that any such quantitative theory of statistics be based upon probability theory. The present state of this theory has benefited greatly from contri­ butions by D. Blackwell and L. LeCam whose fundamental articles expanded the mathematical theory of statistical experiments into the field of com­ parison of experiments. This will be the main motivation for the ap­ proach to the subject taken in this book.

Authors and Affiliations

  • Mathematisches Institut, Universität Tübingen, Tübingen 1, West Germany

    H. Heyer

Bibliographic Information

  • Book Title: Theory of Statistical Experiments

  • Authors: H. Heyer

  • Series Title: Springer Series in Statistics

  • DOI: https://doi.org/10.1007/978-1-4613-8218-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1982

  • Softcover ISBN: 978-1-4613-8220-1Published: 12 October 2011

  • eBook ISBN: 978-1-4613-8218-8Published: 06 December 2012

  • Series ISSN: 0172-7397

  • Series E-ISSN: 2197-568X

  • Edition Number: 1

  • Number of Pages: X, 289

  • Additional Information: Original German edition published in the series: Hochschultext

  • Topics: Applications of Mathematics

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