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Testing Problems with Linear or Angular Inequality Constraints

  • Johan C. Akkerboom

Part of the Lecture Notes in Statistics book series (LNS, volume 62)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Johan C. Akkerboom
    Pages 155-220
  3. Johan C. Akkerboom
    Pages 221-252
  4. Back Matter
    Pages 253-291

About this book

Introduction

Represents a self-contained account of a new promising and generally applicable approach to a large class of one-sided testing problems, where the alternative is restricted by at least two linear inequalities. It highlights the geometrical structure of these problems. It gives guidance in the construction of a so-called Circular Likelihood Ratio (CLR) test, which is obtained if the linear inequalities, or polyhedral cone, are replaced by one suitable angular inequality, or circular cone. Such a test will often constitute a nice and easy-to-use compromise between the LR-test and a suitable linear test against the original alternative. The book treats both theory and practice of CLR-tests. For cases with up to 13 linear inequalities, it evaluates the power of CLR-tests, derives the most stringent CLR-test, and provides tables of critical values. It is of interest both to the specialist in order- restricted inference and to the statistical consultant in need of simple and powerful one-sided tests. Many examples are worked out for ANOVA, goodness-of-fit, and contingency table problems. Case studies are devoted to Mokken's one- dimensional scaling model, one-sided treatment comparison in a two-period crossover trial, and some real data ANOVA- layouts (biology and educational psychology).

Keywords

ANOVA Variance analysis of variance likelihood multinomial distribution statistics

Authors and affiliations

  • Johan C. Akkerboom
    • 1
  1. 1.Department of Statistical MethodsCentral Bureau of StatisticsHeerlenThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-3392-3
  • Copyright Information Springer-Verlag New York 1990
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-97232-9
  • Online ISBN 978-1-4612-3392-3
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site