Testing Homogeneity in Gamma Mixture Models

This paper characterizes the asymptotic behaviour of the likelihood ratio test statistic (LRTS) for testing homogeneity (i.e. no mixture) against gamma mixture alternatives. Under the null hypothesis, the LRTS is shown to be asymptotically equivalent to the square of Davies's Gaussian process test statistic and diverges at a log n rate to infinity in probability. Based on the asymptotic analysis, we propose and demonstrate a computationally efficient method to simulate the null distributions of the LRTS for small to moderate sample sizes.