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

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

2010-12-19

arxiv.org/abs/1012.4183v2

Mathematics

Statistics Theory

Scientific paper

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.

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