Testing the number of components in a normal mixture

Yungtai Lo, Nancy R. Mendell, Donald B. Rubin

Research output: Contribution to journalArticle

1743 Citations (Scopus)

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 A-0-component normal mixture distribution against the alternative hypothesis that the sample is drawn from a A-4-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.

Original languageEnglish (US)
Pages (from-to)767-778
Number of pages12
JournalBiometrika
Volume88
Issue number3
StatePublished - 2001
Externally publishedYes

Fingerprint

Normal Mixture
Normal Distribution
Number of Components
Testing
Mixture Distribution
Likelihood Ratio Statistic
testing
Gaussian distribution
statistics
Statistics
Kullback-Leibler Information
Chi-squared
Information Criterion
Weighted Sums
Regularity Conditions
Limiting Distribution
Random variables
Null hypothesis
Adjustment
Rate of Convergence

Keywords

  • Kullback-Leibler information criterion
  • Likelihood ratio test
  • Normal mixture
  • Weighted sum of chi-squared random variables

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

Cite this

Lo, Y., Mendell, N. R., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88(3), 767-778.

Testing the number of components in a normal mixture. / Lo, Yungtai; Mendell, Nancy R.; Rubin, Donald B.

In: Biometrika, Vol. 88, No. 3, 2001, p. 767-778.

Research output: Contribution to journalArticle

Lo, Y, Mendell, NR & Rubin, DB 2001, 'Testing the number of components in a normal mixture', Biometrika, vol. 88, no. 3, pp. 767-778.
Lo Y, Mendell NR, Rubin DB. Testing the number of components in a normal mixture. Biometrika. 2001;88(3):767-778.
Lo, Yungtai ; Mendell, Nancy R. ; Rubin, Donald B. / Testing the number of components in a normal mixture. In: Biometrika. 2001 ; Vol. 88, No. 3. pp. 767-778.
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