## Bernoulli

• Bernoulli
• Volume 19, Number 5B (2013), 2222-2249.

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

#### Abstract

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 $\mathrm{L}_{q}$-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 $T/\sqrt{N}$.

#### Article information

Source
Bernoulli, Volume 19, Number 5B (2013), 2222-2249.

Dates
First available in Project Euclid: 3 December 2013

https://projecteuclid.org/euclid.bj/1386078601

Digital Object Identifier
doi:10.3150/12-BEJ450

Mathematical Reviews number (MathSciNet)
MR3160552

Zentralblatt MATH identifier
06254560

#### Citation

Dubarry, Cyrille; Le Corff, Sylvain. Non-asymptotic deviation inequalities for smoothed additive functionals in nonlinear state-space models. Bernoulli 19 (2013), no. 5B, 2222--2249. doi:10.3150/12-BEJ450. https://projecteuclid.org/euclid.bj/1386078601

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