A note on the distribution of the likelihood ratio statistic for normal mixture models with known proportions
Athanase Polymenis, D. Michael Titterington · Journal of Statistical Computation and Simulation · 1999
Goffinet et al. (1992) derived the limiting distribution of the likelihood ratio test statistic (LRTS) when testing between a normal distribution and a mixture of two normal distributions with known proportion p. This distribution depends discontinuously on values of p.. Simulations performed by the above authors have shown a very slow convergence towards the theoretical results in the case that p. is close to 0.5. In this paper we shall study the distribution of the LRTS for reasonable sample sizes, and give a heuristic explanation that accounts for the slow convergence.