Springer Series in Statistics

The Linear Model and Hypothesis

A General Unifying Theory

Authors: Seber, George A.F.

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  • Provides a concise and unique overview of hypothesis testing in four important statistical subject areas: linear and nonlinear models, multivariate analysis, and large sample theory
  • Shows that all hypotheses are linear or asymptotically so, and that all the basic models are exact or asymptotically linear normal models. This means that the concept of orthogonality in analysis variance can be extended to other models, and the three standard methods of hypothesis testing, namely the likelihood ratio test, the Wald test and the Score (Lagrange Multiplier) test, can be shown to be asymptotically equivalent for the various models
  • Uses a geometrical approach utilizing the ideas of orthogonal projections  and idempotent  matrices. It avoids some of the complications involved with finding ranks of matrices and provides a simpler and more intuitive approach to the subject matter
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eBook $69.99
price for USA in USD (gross)
  • ISBN 978-3-319-21930-1
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Hardcover $109.99
price for USA in USD
  • ISBN 978-3-319-21929-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA in USD
  • ISBN 978-3-319-34917-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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 involvematrix 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 to other models in the analysis of variance, and to show that the asymptotic equivalence of the likelihood ratio, Wald, and Score (Lagrange Multiplier) hypothesis tests generally applies.

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.

Reviews

“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)


Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-3-319-21930-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-319-21929-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA in USD
  • ISBN 978-3-319-34917-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Linear Model and Hypothesis
Book Subtitle
A General Unifying Theory
Authors
Series Title
Springer Series in Statistics
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-21930-1
DOI
10.1007/978-3-319-21930-1
Hardcover ISBN
978-3-319-21929-5
Softcover ISBN
978-3-319-34917-6
Series ISSN
0172-7397
Edition Number
1
Number of Pages
IX, 205
Topics