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

摘要

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