The linear model and hypothesis: a general unifying theory

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 m...

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Detalles Bibliográficos
Autor principal: Seber, George
Lenguaje:eng
Publicado: Springer 2015
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-21930-1
http://cds.cern.ch/record/2112940
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author Seber, George
author_facet Seber, George
author_sort Seber, George
collection CERN
description 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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spelling cern-21129402021-04-21T20:00:26Zdoi:10.1007/978-3-319-21930-1http://cds.cern.ch/record/2112940engSeber, GeorgeThe linear model and hypothesis: a general unifying theoryMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:21129402015
spellingShingle Mathematical Physics and Mathematics
Seber, George
The linear model and hypothesis: a general unifying theory
title The linear model and hypothesis: a general unifying theory
title_full The linear model and hypothesis: a general unifying theory
title_fullStr The linear model and hypothesis: a general unifying theory
title_full_unstemmed The linear model and hypothesis: a general unifying theory
title_short The linear model and hypothesis: a general unifying theory
title_sort linear model and hypothesis: a general unifying theory
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-21930-1
http://cds.cern.ch/record/2112940
work_keys_str_mv AT sebergeorge thelinearmodelandhypothesisageneralunifyingtheory
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