The Linear Model and Hypothesis: A General Unifying Theory (Springer Series in Statistics) - Hardcover

“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)

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.