The Limiting Distribution of the Restricted Likelihood Ratio Statistic for Finite Mixture Models

The limiting distribution of the likelihood ratio statistic for finite mixture models is not the usual chisquare （Hartigan 1985）. In this paper, we study the limiting distribution under the assumption that the weights of mixture components are larger than a positive number. It is found that the limiting distribution of the new statistic becomes a mixture of chisquares. Simulation study suggests that this limiting distribution approximates the finite sample distribution with reasonably precision.