Non-asymptotic deviation inequalities for smoothed additive functionals in nonlinear state-space models. (English) Zbl 1411.60116

Dubarry, Cyrille; Le Corff, Sylvain

Bernoulli 19, No. 5B, 2222-2249 (2013).

Summary: 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 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 \(T/\sqrt{N}\).

MSC:

60J55	Local time and additive functionals
60J22	Computational methods in Markov chains
62M05	Markov processes: estimation; hidden Markov models

Keywords:

additive functionals; deviation inequalities; FFBS; FFBSi; particle-based approximations; sequential Monte Carlo methods

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