Asymptotic Smoothing errors for Hidden Markov Models

In this paper, the asymptotic smoothing error for hidden Markov models (HMMs) is investigated using hypothesis testing ideas. A family of HMMs is studied parametrised by a positive constant e, which is a measure of the frequency of change. Thus, when e -> 0, the HMM becomes increasingly slower moving. We show that the smoothing error is O(e). These theoretical predictions are confirmed by a series of simulations