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The Linear Model and Hypothesis = A General Unifying Theory /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The Linear Model and Hypothesis/ by George Seber.
Reminder of title:	A General Unifying Theory /
Author:	Seber, George.
Description:	IX, 205 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Statistics . -
Online resource:	https://doi.org/10.1007/978-3-319-21930-1
ISBN:	9783319219301

The Linear Model and Hypothesis = A General Unifying Theory /
Seber, George.

The Linear Model and HypothesisA General Unifying Theory /[electronic resource] :by George Seber. - 1st ed. 2015. - IX, 205 p.online resource. - Springer Series in Statistics,0172-7397. - Springer Series in Statistics,.

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.

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.

ISBN: 9783319219301

Standard No.: 10.1007/978-3-319-21930-1doiSubjects--Topical Terms:

1253516
Statistics .

LC Class. No.: QA276-280

Dewey Class. No.: 519.5

The Linear Model and Hypothesis = A General Unifying Theory /
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520 $a 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.
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