Truncated linear estimation of a bounded multivariate normal mean |
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Authors: | Othmane Kortbi,É ric Marchand |
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Affiliation: | Département de mathématiques, Université de Sherbrooke, Sherbrooke, Qc, Canada J1K 2R1 |
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Abstract: | We consider the problem of estimating the mean θ of an Np(θ,Ip) distribution with squared error loss ∥δ−θ∥2 and under the constraint ∥θ∥≤m, for some constant m>0. Using Stein's identity to obtain unbiased estimates of risk, Karlin's sign change arguments, and conditional risk analysis, we compare the risk performance of truncated linear estimators with that of the maximum likelihood estimator δmle. We obtain for fixed (m,p) sufficient conditions for dominance. An asymptotic framework is developed, where we demonstrate that the truncated linear minimax estimator dominates δmle, and where we obtain simple and accurate measures of relative improvement in risk. Numerical evaluations illustrate the effectiveness of the asymptotic framework for approximating the risks for moderate or large values of p. |
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Keywords: | Restricted parameters Point estimation Squared error loss Dominance Truncated linear estimators Truncated linear minimax Maximum likelihood Multivariate normal Asymptotic analysis |
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