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Activity Number: 600
Type: Contributed
Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #317337
Title: Optimality of the Estimates of the Means After Selection
Author(s): Alexandra Bolotskikh* and Claudio Fuentes and Martin Wells
Companies: Cornell University and Oregon State University and Cornell University
Keywords: Mean estimation ; post-selection inference ; Minimaxity ; Admissibility
Abstract:

Researchers are often interested in making inference on one or a few "best" treatments out of p given treatments. This problem is referred to as post-selection inference. Substantial research has been done on constructing point estimates and confidence sets for a multivariate normal mean vector, but there are very few works on selection. Often, out of all available estimates, the ones that are minimax and/or admissible are preferred. It was proven by Sacrowitz and Samuel-Cahn (1980) that X_1, the first order statistic, is minimax for estimating the selected mean for p< =3, but it is not minimax for p>3, but the question whether it is admissible is still open. Following the arguments of Berger (1976) and Maruyama (2009) we prove that X_1 is admissible for p< 4 and some bias correction is needed for p>=4. The bias corrected estimate, the generalized Bayes estimate under some prior, will be admissible for p>=4. We also provide a comparison of this admissible estimator and other estimators proposed in the literature, including the estimator proposed in Reid et al. (2014) and a generalized Bayes estimator under the horseshoe prior.


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