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On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture

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  • G. J. McLachlan

Abstract

An important but difficult problem in practice is assessing the number of components g in a mixture. An obvious way of proceeding is to use the likelihood ratio test statistic λ to test for the smallest value of g consistent with the data. Unfortunately with mixture models, regularity conditions do not hold for –2 log λ to have it usual asymptotic null distribution of chi‐squared. In this paper the role of the bootstrap is highlighted for the assessment of the null distribution of –2 log λ for the test of a single normal density versus a mixture of two normal densities in the univariate case.

Suggested Citation

  • G. J. McLachlan, 1987. "On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 318-324, November.
  • Handle: RePEc:bla:jorssc:v:36:y:1987:i:3:p:318-324
    DOI: 10.2307/2347790
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