Non-asymptotic deviation inequalities for smoothed additive functionals in non-linear state-space models
Statistics Theory
2012-04-30 v2 Statistics Theory
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.
Cite
@article{arxiv.1012.4183,
title = {Non-asymptotic deviation inequalities for smoothed additive functionals in non-linear state-space models},
author = {Cyrille Dubarry and Sylvain Le Corff},
journal= {arXiv preprint arXiv:1012.4183},
year = {2012}
}