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Activity Number:
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29
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Type:
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Contributed
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Date/Time:
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Sunday, August 6, 2006 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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| Abstract - #307586 |
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Title:
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The Likelihood Ratio Test of Mixture Hypotheses and the Tube Volume Problem
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Author(s):
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Yong Lin*+ and Bruce G. Lindsay
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Companies:
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University of Medicine & Dentistry of New Jersey and The Pennsylvania State University
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Address:
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195 Little Albany Street, New Brunswick, NJ, 08901,
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Keywords:
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mixture hypotheses ; likelihood ratio test ; Hotelling's tube volume ; projection onto cone
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Abstract:
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The testing of the number of components in a mixture model has wide applications. But the distributional properties of likelihood ratio test of the mixture hypotheses have long been an enigma. In this paper, we will consider the testing of s versus t components of mixtures for multinomial models when the parameter is in any finite dimensional space. Based on Lindsay's geometric framework (1995), we will use Hotelling-Naiman's tube volume formula and Weyl's technique to find upper and lower bounds for the upper quantile of the projection of normal vector onto a non-convex cone, and hence give the upper and lower bounds for the upper quantile of the asymptotic distribution of likelihood ratio statistics of the mixture hypotheses. Adequacy of the quantile approximation will be studied. Furthermore, we will apply our results to the mixture of binomial distributions.
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