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Activity Number:
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53
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Type:
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Contributed
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Date/Time:
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Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
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Sponsor:
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General Methodology
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| Abstract - #302170 |
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Title:
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Testing Homogeneity in Discrete Mixtures via L-Two Distances
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Author(s):
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Richard J. Charnigo*+ and Jiayang Sun
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Companies:
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University of Kentucky and Case Western Reserve University
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Address:
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Dept. of Statistics and Division of Biostatistics, Lexington, KY, 40506-0027,
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Keywords:
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D-test ; discrete mixture ; homogeneity ; L-two distance ; mixture distribution
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Abstract:
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The recently developed D-test for homogeneity in continuous mixture distributions is competitive with likelihood ratio tests and easier to employ. We develop a D-test for homogeneity in discrete mixtures. We define a D-test statistic, study its convergence rates under the null and alternative hypotheses, and characterize its asymptotic null distribution under maximum likelihood and penalized maximum likelihood estimation frameworks. As in the continuous case, a generalized or weighted D-test may be performed; while the interpretation is different in the discrete setting, the generalization still allows the D-test to be adapted to the specific parametric family from which the mixture components come. We characterize the asymptotic null distribution of the generalized D-test statistic in the discrete setting and establish that similar results hold in the continuous case. The small-sample applicability of the asymptotic theory as well as the competitiveness of the D-test and its generalization are investigated for Binomial and Poisson mixtures. We also examine an epidemiological dataset that is not adequately described by a homogeneous Poisson model.
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