Asymptotically Efficient Identification of Known-Sensor Hidden Markov Models
This work addresses the need for efficient and statistically optimal estimation in hidden Markov models, a problem relevant to signal processing and time series analysis.
The authors propose a two-step algorithm for estimating the transition probability matrix of a hidden Markov model with known observation probabilities, achieving consistency and asymptotic efficiency while being computationally less demanding than conventional methods, especially for large datasets.
We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. The main contribution is a two-step algorithm; a method of moments estimator (formulated as a convex optimization problem) followed by a single iteration of a Newton-Raphson maximum likelihood estimator. The two-fold contribution of this letter is, firstly, to theoretically show that the proposed estimator is consistent and asymptotically efficient, and secondly, to numerically show that the method is computationally less demanding than conventional methods - in particular for large data sets.