On the robustness of least squares procedures in regression models |
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Authors: | Malay Ghosh Bimal Kumar Sinha |
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Institution: | 1. Indian Statistical Institute India;2. Iowa State University USA |
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Abstract: | The criterion robustness of the standard likelihood ratio test (LRT) under the multivariate normal regression model and also the inference robustness of the same test under the univariate set up are established for certain nonnormal distributions of errors. Restricting attention to the normal distribution of errors in the context of univariate regression models, conditions on the design matrix are established under which the usual LRT of a linear hypothesis (under homoscedasticity of errors) remains valid if the errors have an intraclass covariance structure. The conditions hold in the case of some standard designs. The relevance of C. R. Rao's (1967 In Proceedings Fifth Berkeley Symposium on Math. Stat. and Prob., Vol. 1, pp. 355–372) and G. Zyskind's (1967, Ann. Math. Statist.38 1092–1110) conditions in this context is discussed. |
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Keywords: | 62J05 62H15 Univariate and multivariate regression models least squares procedures maximum likelihood estimates likelihood ratio tests intraclass correlation matrix balanced block designs |
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