Testing the number of components in a normal mixture
2001/10/01 by Y. Lo, Yungtai Lo · 4,573 citations
Computer Science · Mathematics · #Asymptotic distribution #Bayesian Methods and Mixture Models #Component (thermodynamics) #Confidence interval #Convergence (economics) #Distribution (mathematics) #Empirical distribution function #Empirical likelihood #Likelihood-ratio test #Mathematical analysis #Mathematics #Mixture model #Normal distribution #Null distribution #Null hypothesis #Statistic #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistical hypothesis testing #Statistics #Test statistic
paper · doi:10.1093/biomet/88.3.767
published in Biometrika 88(3), 767-778 (Oxford University Press)
openalex publication_date 2001/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract
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 k0‐component normal mixture distribution against the alternative hypothesis that the sample is drawn from a k1‐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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