Sufficient conditions are provided under which the log-likelihood ratio test statistic fails to
have a limiting chi-squared distribution under the null hypothesis when testing between one
and two components under a general two-component mixture model, but rather tends to
infinity in probability. These conditions are verified when the component densities describe
continuous-time, discrete-state-space Markov chains and the results are illustrated via a
parametric bootstrap simulation on an analysis of the migrations over time of a set of …