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

摘要

The approximation of fixed-interval smoothing distributions is a key issue in inference for general statespace 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 L_q-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/N/(1/2).