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Activity Number:
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257
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Type:
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Invited
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Date/Time:
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Tuesday, July 31, 2007 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #307946 |
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Title:
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Frequentist-Bayes Lack-of-Fit Tests Based on a Laplace Approximation
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Author(s):
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Jeffrey Hart*+
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Companies:
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Texas A&M University
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Address:
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Department of Statistics, College Station, TX, 77843,
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Keywords:
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Bayes tests ; Lack-of-fit tests ; Nonparametric tests ; Orthogonal series
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Abstract:
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The no-effect hypothesis in regression is tested in frequentist fashion using as test statistic a Laplace approximation to the posterior probability of this hypothesis. Dependence of the Laplace approximation on prior probabilities allows the investigator to tailor the test to particular alternatives. Use of diffuse priors produces new omnibus lack-of-fit statistics. These omnibus statistics are weighted sums of exponentiated squared (and normalized) Fourier coefficients, where the weights are model prior probabilities. Exponentiation of the Fourier components leads to tests that are much more powerful against higher frequency alternatives than classical tests, such as the cusum, based on weighted sums of squared Fourier coefficients. Our results appear to bring omnibus statistics that involve no choice of smoothing parameters back to the forefront of lack-of-fit testing.
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- Authors who are presenting talks have a * after their name.
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