Testing the number of components in a normal mixture

✍ Scribed by Lo, Y.

• Book ID: 125503752
• Publisher: Oxford University Press
• Year: 2001
• Tongue: English
• Weight: 137 KB
• Volume: 88
• Category: Article
• ISSN: 0006-3444
• DOI: 10.1093/biomet/88.3.767

✦ Synopsis

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.