The Linear Model and Hypothesis
A General Unifying Theory
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Beschreibung
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.
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.
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
Autor*in
George Seber
Themen in »The Linear Model and Hypothesis«
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
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“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)
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