The likelihood ratio test for hidden Markov models in two-sample problems

The asymptotic distribution of the likelihood ratio test statistic in two-sample testing problems for hidden Markov models is derived when allowing for unequal sample sizes as well as for different families of state-dependent distributions. In both cases under regularity conditions the limit distribution is a standard χ2χ2-distribution, and in particular does not depend on the ratio of the distinct sample sizes. In a simulation study, the finite sample properties are investigated, and the methodology is illustrated in an application to modeling the movement of Drosophila larvae.