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

Olsson, Jimmy LU ; Cappé, Olivier; Douc, Randal and Moulines, Éric (2008) In Bernoulli 14(1). p.155-179
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
stochastic volatility model, exponential family, state space models, particle filters, EM algorithm, sequential Monte Carlo methods
in
Bernoulli
volume
14
issue
1
pages
155 - 179
publisher
Chapman and Hall
external identifiers
  • scopus:41449089271
ISSN
1350-7265
DOI
10.3150/07-BEJ6150
language
English
LU publication?
yes
id
150c3923-2aaf-477c-be6c-8d4e1caf3147 (old id 1271937)
date added to LUP
2009-05-28 14:41:14
date last changed
2017-10-29 04:03:10
@article{150c3923-2aaf-477c-be6c-8d4e1caf3147,
  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.},
  author       = {Olsson, Jimmy and Cappé, Olivier and Douc, Randal and Moulines, Éric},
  issn         = {1350-7265},
  keyword      = {stochastic volatility model,exponential family,state space models,particle filters,EM algorithm,sequential Monte Carlo methods},
  language     = {eng},
  number       = {1},
  pages        = {155--179},
  publisher    = {Chapman and Hall},
  series       = {Bernoulli},
  title        = {Sequential Monte Carlo smoothing with application to parameter estimation in nonlinear state space models},
  url          = {http://dx.doi.org/10.3150/07-BEJ6150},
  volume       = {14},
  year         = {2008},
}