Computation of Standard Errors for Maximum-likelihood Estimates in Hidden Markov Models

Explicit computation of the score vector and the observed information matrix in hidden Markov models is described. With the help of the information matrix Wald's con dence intervals can be formed for the model parameters. Finite sample properties of the maximum-likelihood estimator and its standard error are investigated by means of simulation studies. We compare the con dence levels of intervals based on two model estimation methods. The problems in model estimation due to multimodal nature of the likelihood surface are demonstrated and discussed as well. Moreover, using the same approach one can investigate the uncertainty of the classi cation procedure based on the likelihood values in the recognition problems.