Non-asymptotic deviation inequalities for smoothed additive functionals in non-linear state-space models with applications to parameter estimation

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

1 SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
2 LTCI - Laboratoire Traitement et Communication de l'Information

Approximating joint smoothing distributions using particle-based methods is a well-known issue in statistical inference when operating on general state space hidden Markov models (HMM). In this paper we focus on non-asymptotic bounds for the error generated by the computation of smoothed additive functionals. More precisely, this contribution provides new results on the forward filtering backward smoothing (FFBS) Lq-mean errors under appropriate mixing conditions on the Markov kernel's probability density function. The algorithm used has a computational complexity depending linearly on TN where T is the number of observations and N the number of particles. The main improvement concerns the rate of convergence of these norms which depends on T and N only through the ratio T/N for additive functionals (i.e. with norm proportional to T). This paper relies mainly on recent exponential deviation inequalities on the smoothing error.

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

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 with applications to parameter estimation. 2010. ⟨hal-00548092v1⟩