Abstract #302092

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JSM 2003 Abstract #302092
Activity Number: 207
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #302092
Title: Estimation of Variance after Model Selection
Author(s): Vanja M. Dukic*+ and Edsel A. Pena
Companies: University of Chicago and University of South Carolina
Address: Dept. of Health Studies, Room W-260, Chicago, IL, 60637,
Keywords: adaptive estimators ; model selection ; Bayes estimators ; variance estimation
Abstract:

The problem of estimating the variance in a Gaussian model which ranges between a model where the mean parameter is fully known and a model where the mean parameter is completely unknown will be considered. This research is motivated by the desire to understand theoretical implications of the process of selecting a model among several submodels, and then estimating a parameter of interest after model selection, but with these sequential steps using the same sample data. The following are compared: (I) estimators developed under a general model, and in the extreme case, under a fully nonparametric model; (II) two-step estimators, comprised of a model selector and an estimator developed under the chosen submodel, with both steps using the same sample data; and (III) estimators based on a weighted combination of all submodel estimators. It will be shown that efficiency gains can be obtained by exploiting the submodel structure, especially when the number of competing submodels is low, but that this advantage may deteriorate as the number of submodels increases.

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