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The linear model and hypothesis = a ...

Seber, George A.F.

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The linear model and hypothesis = a general unifying theory /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The linear model and hypothesis/ by George A.F. Seber.
Reminder of title:	a general unifying theory /
Author:	Seber, George A.F.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	ix, 205 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Linear models (Statistics) -
Online resource:	http://dx.doi.org/10.1007/978-3-319-21930-1
ISBN:	9783319219301

The linear model and hypothesis = a general unifying theory /
Seber, George A.F.

The linear model and hypothesisa general unifying theory /[electronic resource] :by George A.F. Seber. - Cham :Springer International Publishing :2015. - ix, 205 p. :ill., digital ;24 cm. - 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:

533190
Linear models (Statistics)

LC Class. No.: QA276

Dewey Class. No.: 519.535

The linear model and hypothesis = a general unifying theory /
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100 1 $a Seber, George A.F. $3 2162978
245 1 4 $a The linear model and hypothesis $h [electronic resource] : $b a general unifying theory / $c by George A.F. Seber.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a ix, 205 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer series in statistics, $x 0172-7397
505 0 $a 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.
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.
650 0 $a Linear models (Statistics) $3 533190
650 0 $a Statistical hypothesis testing. $3 560235
650 0 $a Mathematical statistics. $3 516858
650 1 4 $a Statistics. $3 517247
650 2 4 $a Statistical Theory and Methods. $3 891074
650 2 4 $a Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law. $3 894294
710 2 $a SpringerLink (Online service) $3 836513
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830 0 $a Springer series in statistics. $3 1315057
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-21930-1
950 $a Mathematics and Statistics (Springer-11649)