Asymptotical statistics of misspecified HMM
Laurent Mevel, Lorenzo Finesso · Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) · 2003
Deals with the fitting of hidden Markov models to data generated by ergodic stochastic processes. More specifically we consider the problem of fitting a family of partially observed finite state Markov chain parameters (or hidden Markov models, HMMs) with continuous output to an ergodic process, with continuous values, which is not necessarily a member of the family. In this context we derive the main asymptotic results: almost sure consistency, asymptotic normality and rate of convergence of the MLE estimator.