On a Resampling Approach to Choosing the Number of Components in Normal Mixture Models

We consider the tting of a g-component normal mixture to multivariate data. The problem is to test whether g is equal to some speciied value versus some speciied alternative value. This problem would arise, for example, in the context of a cluster analysis eeected by a normal mixture model, where the decision on the number of clusters is undertaken by testing for the smallest value of g compatible with the data. A test statistic can be formed in terms of the likelihood ratio. Unfortunately, regularity conditions do not hold for the likelihood ratio statistic to have its usual asymptotic null distribution of chi-squared. One approach to the assessment of P-values with the use of this statistic is to adopt a resampling approach. An investigation is undertaken of the accuracy of P-values assessed in this manner.