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Activity Number:
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308
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Type:
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Invited
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Date/Time:
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Tuesday, July 31, 2007 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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| Abstract - #307868 |
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Title:
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Multiple Shrinkage Predictive Densities for Linear Regression Models
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Author(s):
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Xinyi Xu*+ and Edward I. George
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Companies:
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The Ohio State University and University of Pennsylvania
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Address:
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Department of Statistics, Columbus, OH, 43210-1247,
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Keywords:
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density prediction ; model uncertainty ; Bayesian model averaging ; multiple shrinkage
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Abstract:
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In this talk, we consider the problem of estimating the predictive density of a future quantity of interest based on a linear regression model, where exists a large number of predictors but only some of them are potentially relevant. Bayesian Model Averaging (BMA) is a general and powerful tool in this context since it incorporates model uncertainty by averaging over competing models with different predictor sets. We use the BMA approach to construct a class of multiple shrinkage predictive densities that dominate the "noninformative" uniform prior Bayes procedure and therefore are minimax. We also show that these multiple shrinkage predictive densities adaptively shrink toward the model most favored by the data, and achieve minimal risks under different degrees of model sparsity.
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