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The Linear Model and Hypothesis

A General Unifying Theory

  • George Seber

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

Table of contents

  1. Front Matter
    Pages i-ix
  2. George A. F. Seber
    Pages 1-19
  3. George A. F. Seber
    Pages 21-26
  4. George A. F. Seber
    Pages 27-45
  5. George A. F. Seber
    Pages 47-60
  6. George A. F. Seber
    Pages 61-71
  7. George A. F. Seber
    Pages 73-101
  8. George A. F. Seber
    Pages 103-116
  9. George A. F. Seber
    Pages 117-128
  10. George A. F. Seber
    Pages 129-147
  11. George A. F. Seber
    Pages 149-174
  12. George A. F. Seber
    Pages 175-179
  13. George A. F. Seber
    Pages 181-188
  14. Back Matter
    Pages 189-205

About this book

Introduction

This book provides a concise and integrated overview of hypothesis testing in four important subject areas, namely linear and nonlinear models, multivariate analysis, and large sample theory. The approach used is a geometrical one based on the concept of projections and their associated idempotent matrices, thus largely avoiding the need to involve matrix ranks. It is shown that all the hypotheses encountered are either linear or asymptotically linear, and that all the underlying models used are either exactly or asymptotically linear normal models. This equivalence can be used, for example, to extend the concept of orthogonality in the analysis of variance to other models, and to show that the asymptotic equivalence of the likelihood ratio, Wald, and Score (Lagrange Multiplier) hypothesis tests generally applies.

Keywords

Analysis of variance Goodness-of-fit test. Hypothesis tests Lagrange multiplier test Large sample tests Likelihood ratio test Linear models Missing observations Multinomial distribution Multivariate hypothesis testing Orthogonal projections Score test Separable hypotheses Simultaneous confidence intervals Wald test

Authors and affiliations

  • George Seber
    • 1
  1. 1.Department of StatisticsThe University of AucklandAucklandNew Zealand

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-21930-1
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-21929-5
  • Online ISBN 978-3-319-21930-1
  • Series Print ISSN 0172-7397
  • Series Online ISSN 2197-568X
  • Buy this book on publisher's site
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