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Goodness-of-Fit Statistics for Discrete Multivariate Data

  • Timothy R. C. Read
  • Noel A. C. Cressie

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Timothy R. C. Read, Noel A. C. Cressie
    Pages 1-4
  3. Timothy R. C. Read, Noel A. C. Cressie
    Pages 5-18
  4. Timothy R. C. Read, Noel A. C. Cressie
    Pages 19-43
  5. Timothy R. C. Read, Noel A. C. Cressie
    Pages 44-63
  6. Timothy R. C. Read, Noel A. C. Cressie
    Pages 64-80
  7. Timothy R. C. Read, Noel A. C. Cressie
    Pages 81-97
  8. Timothy R. C. Read, Noel A. C. Cressie
    Pages 98-113
  9. Timothy R. C. Read, Noel A. C. Cressie
    Pages 114-132
  10. Timothy R. C. Read, Noel A. C. Cressie
    Pages 133-153
  11. Back Matter
    Pages 154-211

About this book

Introduction

The statistical analysis of discrete multivariate data has received a great deal of attention in the statistics literature over the past two decades. The develop­ ment ofappropriate models is the common theme of books such as Cox (1970), Haberman (1974, 1978, 1979), Bishop et al. (1975), Gokhale and Kullback (1978), Upton (1978), Fienberg (1980), Plackett (1981), Agresti (1984), Goodman (1984), and Freeman (1987). The objective of our book differs from those listed above. Rather than concentrating on model building, our intention is to describe and assess the goodness-of-fit statistics used in the model verification part of the inference process. Those books that emphasize model development tend to assume that the model can be tested with one of the traditional goodness-of-fit tests 2 2 (e.g., Pearson's X or the loglikelihood ratio G ) using a chi-squared critical value. However, it is well known that this can give a poor approximation in many circumstances. This book provides the reader with a unified analysis of the traditional goodness-of-fit tests, describing their behavior and relative merits as well as introducing some new test statistics. The power-divergence family of statistics (Cressie and Read, 1984) is used to link the traditional test statistics through a single real-valued parameter, and provides a way to consolidate and extend the current fragmented literature. As a by-product of our analysis, a new 2 2 statistic emerges "between" Pearson's X and the loglikelihood ratio G that has some valuable properties.

Keywords

Chi-squared distribution Estimator Likelihood Variance best fit information theory multinomial distribution

Authors and affiliations

  • Timothy R. C. Read
    • 1
  • Noel A. C. Cressie
    • 2
  1. 1.Hewlett-Packard CompanyPalo AltoUSA
  2. 2.Department of StatisticsIowa State UniversityAmesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4578-0
  • Copyright Information Springer-Verlag New York 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8931-9
  • Online ISBN 978-1-4612-4578-0
  • Series Print ISSN 0172-7397
  • Buy this book on publisher's site