The Linear Model and Hypothesis: A General Unifying Theory

✍ Scribed by George Seber (auth.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 208
• Series: Springer Series in Statistics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-ix
Preliminaries....Pages 1-19
The Linear Hypothesis....Pages 21-26
Estimation....Pages 27-45
Hypothesis Testing....Pages 47-60
Inference Properties....Pages 61-71
Testing Several Hypotheses....Pages 73-101
Enlarging the Model....Pages 103-116
Nonlinear Regression Models....Pages 117-128
Multivariate Models....Pages 129-147
Large Sample Theory: Constraint-Equation Hypotheses....Pages 149-174
Large Sample Theory: Freedom-Equation Hypotheses....Pages 175-179
Multinomial Distribution....Pages 181-188
Back Matter....Pages 189-205

✦ Subjects

Statistical Theory and Methods; Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law