A Note on the Aitkin-Rubin Approach to Hypothesis Testing in Mixture Models
Barry G. Quinn, Geoffrey John McLachlan, Nils Lid Hjort · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1987
SUMMARY In testing for the number of components in a mixture, it is well known that regularity conditions do not hold for minus twice the log likelihood ratio to have its usual asymptotic null distribution of chi-squared. In an attempt to overcome some of the problems, it has been proposed in the literature that a prior distribution be placed on the mixing proportions. We show here that the usual regularity conditions still do not hold.