Testing for the number of states in hidden Markov models with application to ion channel data

Noisy data recorded from ion channels can be adequately modelled by hidden Markov models with a finite number of states. We address the problem of testing for the number of hidden states by means of the likelihood ratio test. Under the null hypothesis some parameters are on the boundary of the parameter space or some parameters are only identifiable under the alternative, and therefore the likelihood ratio tests have to be applied under nonstandard conditions. The exact asymptotic distribution of the likelihood ratio statistic cannot be derived analytically. Thus, we investigate its asymptotic distribution by simulation studies. We apply these tests to data recorded from potassium channels.