© 2015

The Linear Model and Hypothesis

A General Unifying Theory


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


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.


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

  1. 1.Department of StatisticsThe University of AucklandAucklandNew Zealand

About the authors

George Seber is an Emeritus Professor of Statistics at Auckland University, New Zealand. He is an elected Fellow of the Royal Society of New Zealand, recipient of their Hector medal in Information Science, and recipient of an international Distinguished Statistical Ecologist Award. He has authored or coauthored 16 books and 90 research articles on a wide variety of topics including linear and nonlinear models, multivariate analysis, matrix theory for statisticians, large sample theory, adaptive sampling, genetics, epidemiology, and statistical ecology.

Bibliographic information


“The book deals with the classical topic of multivariate linear models. … the monograph is a consistent, logical and comprehensive treatment of the theory of linear models aimed at scientists who already have a good knowledge of the subject and are well trained in application of matrix algebra.” (Jurgita Markeviciute, zbMATH 1371.62002, 2017)

“This monograph is a welcome update of the author's 1966 book. It contains a wealth of material and will be of interest to graduate students, teachers, and researchers familiar with the 1966 book.” (William I. Notz, Mathematical Reviews, June, 2016)