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Some properties of the relative squared error approach to linear regression analysis
Authors:Bernhard F. Arnold  Peter Stahlecker
Affiliation:1. arnold@econ.uni-hamburg.de
Abstract:In order to obtain optimal estimators in a generalized linear regression model we apply the minimax principle to the relative squared error. It turns out that this approach is equivalent to the application of the minimax principle to the absolute squared error when an ellipsoidal prior information set is given. We discuss the admissibility of these minimax estimators. Furthermore, a close relation to a Bayesian approach is derived.
Keywords:Admissibility  Bayesian estimation  Linear regression  Löwner ordering  Minimax estimation  Prior information  Relative squared error  Ridge regression
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