Likelihood ratio tests of the number of components in a normal mixture with unequal variances

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

Determining the number of components in a mixture distribution is of interest to researchers in many areas. In this paper, we investigate the statistical properties of a likelihood ratio test proposed by Lo et al. (Biometrika 88 (2001) 767) for determining the number of components in a normal mixture with unequal variances. We discuss the dependence of the rate of convergence of the likelihood ratio statistic to its limiting distribution on the choice of restrictions imposed on the component variances to deal with the problem of unboundedness of the likelihood. We compare the test procedure to the parametric bootstrap method and posterior predictive checks, a Bayesian model checking procedure.

Original languageEnglish (US)
Pages (from-to)225-235
Number of pages11
JournalStatistics and Probability Letters
Volume71
Issue number3
DOIs
StatePublished - Mar 1 2005

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Normal Mixture
Number of Components
Likelihood Ratio Test
Unequal
Parametric Bootstrap
Mixture Distribution
Likelihood Ratio Statistic
Variance Components
Bootstrap Method
Bayesian Model
Limiting Distribution
Statistical property
Model Checking
Likelihood
Rate of Convergence
Restriction
Likelihood ratio test
Bayesian model
Limiting distribution
Variance components

Keywords

  • Bootstrap test
  • Likelihood ratio test
  • Normal mixture
  • Posterior predictive checks

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

Likelihood ratio tests of the number of components in a normal mixture with unequal variances. / Lo, Yungtai.

In: Statistics and Probability Letters, Vol. 71, No. 3, 01.03.2005, p. 225-235.

Research output: Contribution to journalArticle

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