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

2010/12/19 by Cyrille Dubarry, Dubarry, Cyrille, Sylvain Le Corff +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.1012.4183

openalex publication_date 2010/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Lq-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 and the square root of N.

Cited by

• On the two-filter approximations of marginal smoothing distributions in\n general state space models

Related

• On the Forward Filtering Backward Smoothing particle approximations of the smoothing distribution in general state spaces models
• Consistent estimation of the filtering and marginal smoothing\n distributions in nonparametric hidden Markov models
• Forward Smoothing using Sequential Monte Carlo
• Smoothing with Couplings of Conditional Particle Filters
• Approximate Bayesian Computation for Smoothing