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

G. J. McLachlan
Journal of the Royal Statistical Society. Series C (Applied Statistics)
Vol. 36, No. 3 (1987), pp. 318-324
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2347790
Stable URL: http://www.jstor.org/stable/2347790
Page Count: 7
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On Bootstrapping the Likelihood Ratio Test Stastistic for the Number of Components in a Normal Mixture
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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 logλ 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.

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