Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Series in Statistics (SSS)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (12 chapters)
-
Front Matter
-
Back Matter
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
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.
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)
Authors and Affiliations
About the author
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
Book Title: The Linear Model and Hypothesis
Book Subtitle: A General Unifying Theory
Authors: George Seber
Series Title: Springer Series in Statistics
DOI: https://doi.org/10.1007/978-3-319-21930-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-21929-5Published: 16 October 2015
Softcover ISBN: 978-3-319-34917-6Published: 23 August 2016
eBook ISBN: 978-3-319-21930-1Published: 08 October 2015
Series ISSN: 0172-7397
Series E-ISSN: 2197-568X
Edition Number: 1
Number of Pages: IX, 205
Topics: Statistical Theory and Methods, Statistics for Social Sciences, Humanities, Law