Asymptotic Smoothing Errors for Hidden Markov Models

In this paper, the asymptotic smoothing error for hidden Markov models (HMM) is investigated using hypothesis testing ideas. A family of HMMs is studied parametrised by a positive constant , which is a measure of the frequency of change. Thus when ! 0, the HMM becomes slower and slower moving. We show that the smoothing error is O(). These theoretical predictions are conrmed by a series of simulations. Key Words: hidden Markov model, smoothing, asymptotic error EDICS classication: SP 3.8.1 The authors wish to acknowledge the funding of the activities of the Cooperative Research Centre for Robust and Adaptive Systems by the Australian Commonwealth Government under the Cooperative Research Centres Program y Department of Systems Engineering and Cooperative Research Centre for Robust and Adaptive Systems, Research School of Information Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia. z Fax: +61-2-6279-8688, Email: Louis.Shue@anu.edu.a..