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

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

Cyrille Dubarry and Sylvain Le Corff

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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 $T/\sqrt{N}$.

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

First available in Project Euclid: 3 December 2013

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


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.

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