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December 2013 A general theory of particle filters in hidden Markov models and some applications
Hock Peng Chan, Tze Leung Lai
Ann. Statist. 41(6): 2877-2904 (December 2013). DOI: 10.1214/13-AOS1172

Abstract

By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated dependence among the sample paths, the asymptotic variance formula and martingale representations lead to consistent estimates of the standard errors of the particle filter estimates of the hidden states.

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Hock Peng Chan. Tze Leung Lai. "A general theory of particle filters in hidden Markov models and some applications." Ann. Statist. 41 (6) 2877 - 2904, December 2013. https://doi.org/10.1214/13-AOS1172

Information

Published: December 2013
First available in Project Euclid: 17 December 2013

zbMATH: 1293.60071
MathSciNet: MR3161451
Digital Object Identifier: 10.1214/13-AOS1172

Subjects:
Primary: 60F10, 65C05
Secondary: 60J22, 60K35

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 6 • December 2013
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