期刊
BIOMETRIKA
卷 88, 期 3, 页码 767-778出版社
BIOMETRIKA TRUST
DOI: 10.1093/biomet/88.3.767
关键词
Kullback-Leibler information criterion; likelihood ratio test; normal mixture; weighted sum of chi-squared random variables
We demonstrate that, under a theorem proposed by Vuong, the likelihood ratio statistic based on the Kullback-Leibler information criterion of the null hypothesis that a random sample is drawn from a k(0)-component normal mixture distribution against the alternative hypothesis that the sample is drawn from a k(1)-component normal mixture distribution is asymptotically distributed as a weighted sum of independent chi-squared random variables with one degree of freedom, under general regularity conditions. We report simulation studies of two cases where we are testing a single normal versus a two-component normal mixture and a two-component normal mixture versus a three-component normal mixture. An empirical adjustment to the likelihood ratio statistic is proposed that appears to improve the rate of convergence to the limiting distribution.
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