Non-asymptotic deviation inequalities for smoothed additive functionals in non-linear state-space models.

Cyrille Dubarry (1, 2) , Sylvain Le Corff (3)

1 SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
2 CNRS - Centre National de la Recherche Scientifique
3 LTCI - Laboratoire Traitement et Communication de l'Information

The approximation of fixed-interval smoothing distributions is a key issue in inference for general state-space hidden Markov models (HMM). This contribution establishes non-asymptotic bounds for the Forward Filtering Backward Smoothing (FFBS) and the Forward Filtering Backward Simulation (FFBSi) estimators of fixed-interval smoothing functionals. We show that the rate of convergence of the Lq-mean errors of both methods depends on the number of observations T and the number of particles N only through the ratio T/N for additive functionals. In the case of the FFBS, this improves recent results providing bounds depending on T and the square root of N.

Mots clés: Additive functionals; Particle-based approximations; Deviation inequalities; Sequential Monte Carlo methods; FFBS; FFBSi

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Cyrille Dubarry, Sylvain Le Corff. Non-asymptotic deviation inequalities for smoothed additive functionals in non-linear state-space models.. Bernoulli, 2013, 19 (5B), pp.2222-2249. ⟨hal-00548092v2⟩