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Activity Number:
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95
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Type:
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Topic Contributed
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Date/Time:
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Monday, August 4, 2008 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #301107 |
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Title:
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Asymptotic Comparisons of Predictive Densities for Dependent Observations
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Author(s):
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Xuanyao He*+ and Richard L. Smith and Zhengyuan Zhu
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Companies:
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The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
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Address:
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Dept of STOR, Chapel Hill, NC, 27599-3260,
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Keywords:
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Mixed effect models ; Kullback-Leibler divergence ; Jeffreys prior ; Predictive density ; Prediction fit
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Abstract:
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This paper studies Bayesian predictive densities based on different priors and frequentist plug-in type predictive densities when the predicted variables are dependent on the observations. Average Kullback-Leibler divergence to the true predictive density is used to measure the performance of different inference procedures. The notion of second-order KL dominance is introduced, and an explicit condition for a prior to be second-order KL dominant is given using an asymptotic expansion. As an example, we show theoretically that for mixed effects models, the Bayesian predictive density with prior from a particular improper prior family dominates the performance of REML plug-in density, while the Jeffrey's prior is not always superior to the REML approach. Simulation studies are included which show good agreement with the asymptotic results for moderate sample size.
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