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Abstract Details
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Activity Number:
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670
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Type:
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Contributed
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Date/Time:
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Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #301158 |
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Title:
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Minimax Risk of Predictive Density Estimation Over L_P Balls
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Author(s):
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Gourab Mukherjee*+ and Iain M. Johnstone
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Companies:
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Stanford University and Stanford University
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Address:
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, , CA, 94305,
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Keywords:
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Predictive Density ;
Minimax ;
Sparse ;
Cluster prior ;
Plugin Risk
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Abstract:
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We consider estimating the predictive density, under Kullback-Leibler loss, for a Gaussian sequence model with known variances. The parametric spaces are assumed to be l_p balls with p in [0, \infty]. We derive exact evaluations of the minimax risk and least favorable prior distribution as signal-to-noise ratio (radius of the ball) and nature of sparsity (p) of the parametric space varies. Comparing predictive minimax risk with optimal plugin risk in very low signal-to-noise ratio regime, we found that a Bayes predictive density based on cluster prior outperforms plug-in densities in sparse parametric spaces (p < 2) whereas in comparatively dense spaces (p>=2) linear plug-in estimators achieve asymptotic minimaxity. The results here can be contrasted to issues seen in estimation of the normal mean under square error loss.
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