Bernoulli

  • Bernoulli
  • Volume 14, Number 1 (2008), 155-179.

Sequential Monte Carlo smoothing with application to parameter estimation in nonlinear state space models

Jimmy Olsson, Olivier Cappé, Randal Douc, and Éric Moulines

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Abstract

This paper concerns the use of sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well-known problem when applying the standard SMC technique in the smoothing mode is that the resampling mechanism introduces degeneracy of the approximation in the path space. However, when performing maximum likelihood estimation via the EM algorithm, all functionals involved are of additive form for a large subclass of models. To cope with the problem in this case, a modification of the standard method (based on a technique proposed by Kitagawa and Sato) is suggested. Our algorithm relies on forgetting properties of the filtering dynamics and the quality of the estimates produced is investigated, both theoretically and via simulations.

Article information

Source
Bernoulli, Volume 14, Number 1 (2008), 155-179.

Dates
First available in Project Euclid: 8 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1202492789

Digital Object Identifier
doi:10.3150/07-BEJ6150

Mathematical Reviews number (MathSciNet)
MR2401658

Zentralblatt MATH identifier
1155.62055

Keywords
EM algorithm exponential family particle filters sequential Monte Carlo methods state space models stochastic volatility model

Citation

Olsson, Jimmy; Cappé, Olivier; Douc, Randal; Moulines, Éric. Sequential Monte Carlo smoothing with application to parameter estimation in nonlinear state space models. Bernoulli 14 (2008), no. 1, 155--179. doi:10.3150/07-BEJ6150. https://projecteuclid.org/euclid.bj/1202492789


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