A likelihood ratio test of a homoscedastic normal mixture against a heteroscedastic normal mixture |
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Authors: | Yungtai Lo |
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Institution: | (1) Department of Community and Preventive Medicine, Mount Sinai School of Medicine, One Gustave L. Levy Place, Box 1057, New York, NY 10029, USA |
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Abstract: | It is generally assumed that the likelihood ratio statistic for testing the null hypothesis that data arise from a homoscedastic
normal mixture distribution versus the alternative hypothesis that data arise from a heteroscedastic normal mixture distribution
has an asymptotic χ
2 reference distribution with degrees of freedom equal to the difference in the number of parameters being estimated under
the alternative and null models under some regularity conditions. Simulations show that the χ
2 reference distribution will give a reasonable approximation for the likelihood ratio test only when the sample size is 2000
or more and the mixture components are well separated when the restrictions suggested by Hathaway (Ann. Stat. 13:795–800,
1985) are imposed on the component variances to ensure that the likelihood is bounded under the alternative distribution. For
small and medium sample sizes, parametric bootstrap tests appear to work well for determining whether data arise from a normal
mixture with equal variances or a normal mixture with unequal variances. |
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Keywords: | Likelihood ratio test Normal mixture Bootstrap EM algorithm |
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