On the Robustness of the LRT with Respect to Specification Errors in a Linear Model

We consider the linear model$(\mathbf{\mathit{Y}},\mathbf{\mathit{X}}\boldsymbol{\beta},\sigma ^{2}\mathbf{\mathit{I}})$and a set of estimable parametric functionals Aβ. In this paper, we consider alternative linear models which differ from$(\mathbf{\mathit{Y}},\mathbf{\mathit{X}}\boldsymbol{\beta},...

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Veröffentlicht in:	Sankhya. Series A 1983-06, Vol.45 (2), p.212-225
Hauptverfasser:	Mathew, Thomas, Bhimasankaram, P.
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Sprache:	eng
Schlagworte:	Covariance matrices Eigenvalues Eigenvectors Linear models Mathematical theorems Mathematical vectors Matrices Statistical theories Statistics Sufficient conditions
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description	We consider the linear model$(\mathbf{\mathit{Y}},\mathbf{\mathit{X}}\boldsymbol{\beta},\sigma ^{2}\mathbf{\mathit{I}})$and a set of estimable parametric functionals Aβ. In this paper, we consider alternative linear models which differ from$(\mathbf{\mathit{Y}},\mathbf{\mathit{X}}\boldsymbol{\beta},\sigma ^{2}\mathbf{\mathit{I}})$in the dispersion of the observations or expectation or both and obtain necessary and sufficient conditions for the F-test under$(\mathbf{\mathit{Y}},\mathbf{\mathit{X}}\boldsymbol{\beta},\sigma ^{2}\mathbf{\mathit{I}}$for testing$H_{0}$: Aβ = 0 to be valid under the alternative model also.
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source	JSTOR Mathematics & Statistics; Jstor Complete Legacy
subjects	Covariance matrices Eigenvalues Eigenvectors Linear models Mathematical theorems Mathematical vectors Matrices Statistical theories Statistics Sufficient conditions
title	On the Robustness of the LRT with Respect to Specification Errors in a Linear Model
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