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Activity Number:
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123
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Type:
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Invited
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Date/Time:
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Monday, August 7, 2006 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #305048 |
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Title:
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On Posterior Consistency in Nonparametric Regression Problems
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Author(s):
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Taeryon Choi*+
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Companies:
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University of Maryland Baltimore County
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Address:
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Department of Mathematics and Statistics, Baltimore, MD, 21250,
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Keywords:
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almost sure consistency ; Hellinger metric ; in probability metric ; empirical probability measure ; sieve ; differentiable functions
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Abstract:
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We give sufficient conditions to establish posterior consistency in nonparametric regression problems with Gaussian error when suitable prior distributions are used for the unknown regression function and noise variance. When the prior under consideration satisfies certain properties, the crucial condition for posterior consistency is to construct tests that make the true parameter separate from the outside of the suitable neighborhoods of the parameter. Under appropriate conditions on the regression function, we show there exist tests of which the type I and type II error probabilities are exponentially small for distinguishing the true parameter from the complements of the suitable neighborhoods of the parameter. We consider two examples of nonparametric regression problems.
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