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JAMES-STEIN RULE ESTIMATORS IN LINEAR REGRESSION MODELS WITH MULTIVARIATE-t DISTRIBUTED ERROR
Authors:Radhey S.  Singh
Affiliation:Dept. Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada.
Abstract:This paper considers estimation of β in the regression model y =+μ, where the error components in μ have the jointly multivariate Student-t distribution. A family of James-Stein type estimators (characterised by nonstochastic scalars) is presented. Sufficient conditions involving only X are given, under which these estimators are better (with respect to the risk under a general quadratic loss function) than the usual minimum variance unbiased estimator (MVUE) of β. Approximate expressions for the bias, the risk, the mean square error matrix and the variance-covariance matrix for the estimators in this family are obtained. A necessary and sufficient condition for the dominance of this family over MVUE is also given.
Keywords:Linear regression model    James-Stein estimators    multivariate Student-2 distribution    unique MVUE    double k-class estimators    bias    mean square error    variance-covariance matrix
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