The Linear Model and Hypothesis

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

Auteur

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.

Contenu

1.Preliminaries.- 2. The Linear Hypothesis.- 3.Estimation.- 4.Hypothesis Testing.- 5.Inference Properties.- 6.Testing Several Hypotheses.- 7.Enlarging the Model.- 8.Nonlinear Regression Models.- 9.Multivariate Models.- 10.Large Sample Theory: Constraint-Equation Hypotheses.- 11.Large Sample Theory: Freedom-Equation Hypotheses.- 12.Multinomial Distribution.- Appendix.- Index.