Fast computation of smoothed additive functionals in general state-space models

Approximating fixed-interval 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 the computation of path-space smoothed additive functionals. More precisely, this contribution provides new results on the forward filtering backward smoothing (FFBS) and the forward filtering backward simulation (FFBSi) algorithms. We prove that the L_q-mean error convergence rate of both algorithms depends on the number of observations T and the number of particles N only through the ratio T/N. We also derive non-asymptotic exponential deviation inequalities for these algorithms. The FFBS and FFBSi algorithms are compared when applied to parameter estimation in HMM.