On the estimation of a restricted normal mean |
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| Affiliation: | 1. Michigan State University and NBER, United States;2. Cornell University and NBER, United States;1. Department of Economics, Pennsylvania State University, University Park, PA, United States;2. Department of Economics, University of Wisconsin, Madison, WI, United States;1. Michigan State Department of Economics, 110 Marshall-Adams Hall, 486 W. Circle Drive, East Lansing, MI 48824, USA;2. Department of Policy Analysis and Management, 102 Martha Van Rensselaer Hall, Ithaca, NY 14853, USA |
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| Abstract: | Let X ∼ N(θ,1), where θ ϵ [−m, m], for some m > 0, and consider the problem of estimating θ with quadratic loss. We show that the Bayes estimator δm, corresponding to the uniform prior on [−m, m], dominates δ0 (x) = x on [−m, m] and it also dominates the MLE over a large part of the parameter interval. We further offer numerical evidence to suggest that δm has quite satisfactory risk performance when compared with the minimax estimators proposed by Casella and Strawderman (1981) and the estimators proposed by Bickel (1981). |
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