2015/01/20 by Yohann de Castro, De Castro, Yohann, Élisabeth Gassiat +3 · 2 citations
Computer Science · Mathematics · #Algorithms and Data Compression #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1501.04787
openalex publication_date 2015/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider stationary hidden Markov models with finite state space and nonparametric modeling of the emission distributions. It has remained unknown until very recently that such models are identifiable. In this paper, we propose a new penalized least-squares esti-mator for the emission distributions which is statistically optimal and practically tractable. We prove a non asymptotic oracle inequality for our nonparametric estimator of the emission distributions. A consequence is that this new estimator is rate minimax adaptive up to a logarithmic term. Our methodology is based on projections of the emission distributions onto nested subspaces of increasing complexity. The popular spectral estimators are unable to achieve the optimal rate but may be used as initial points in our procedure. Simulations are given that show the improvement obtained when applying the least-squares minimization consecutively to the spectral estimation.