Séminaire de Probabilités et Statistique :

Le 03 février 2025 à 13:45 - UM - Bât 09 - Salle 109 (1er étage)

Présentée par Lecestre Alexandre - Inrae Montpellier

Robust estimation in finite state space hidden Markov models

Hidden Markov Models (HMMs) are powerful tools for modeling time-dependent phenomena governed by underlying dynamic processes that are only partially observable. However, standard estimation techniques for HMMs- such as maximum likelihood, least square and spectral methods- often suffer from sensitivity to model misspecification, outliers, and data contamination, resulting in unreliable parameter estimates. To overcome these challenges, we introduce a novel estimation method based on rho-estimators, a class of robust estimators developed by Baraud et al. [1, 2] for independent settings. We prove a non-asymptotic bound on the Hellinger distance between the target distribution and our estimator. It allows us to derive a minimax convergence rate (up to a logarithmic factor) in the well-specified case. We establish the robustness of the estimator by demonstrating that its performance remains stable under contamination, as long as the contamination rate is moderate, regardless of the type of contamination. We can notice a posteriori that the proposed method is not restricted to HMMs and can be generalized to other models satisfying similar properties. For instance, we obtain results for the estimation of the stationary distribution for a class of Langevin diffusions.

Séminaire en salle 109, également retransmis sur zoom : https://umontpellier-fr.zoom.us/j/7156708132