Empirical Bayes estimation in a multiple linear regression model |
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Authors: | R S Singh |
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Institution: | (1) University of Guelph, Guelph, Canada |
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Abstract: | Summary Estimation of the vector β of the regression coefficients in a multiple linear regressionY=Xβ+ε is considered when β has a completely unknown and unspecified distribution and the error-vector ε has a multivariate standard
normal distribution. The optimal estimator for β, which minimizes the overall mean squared error, cannot be constructed for
use in practice. UsingX, Y and the information contained in the observation-vectors obtained fromn independent past experiences of the problem, (empirical Bayes) estimators for β are exhibited. These estimators are compared
with the optimal estimator and are shown to be asymptotically optimal. Estimators asymptotically optimal with rates nearO(n
−1) are constructed.
Supported in part by a Natural Sciences and Engineering Research Council of Canada grant. |
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Keywords: | Empirical Bayes estimation multiple regression model squared error loss asymptotically optimal rates |
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