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Asymptotic properties of particle filter-based maximum likelihood estimators for state space models

Olsson, Jimmy LU and Rydén, Tobias LU (2008) In Stochastic Processes and their Applications 118(4). p.649-680
Abstract
We study the asymptotic performance of approximate maximum likelihood estimators for state space models obtained via sequential Monte Carlo methods. The state space of the latent Markov chain and the parameter space are assumed to be compact. The approximate estimates are computed by, firstly, running possibly dependent particle filters on a fixed grid in the parameter space, yielding a pointwise approximation of the log-likelihood function. Secondly, extensions of this approximation to the whole parameter space are formed by means of piecewise constant functions or B-spline interpolation, and approximate maximum likelihood estimates are obtained through maximization of the resulting functions. In this setting we formulate criteria for how... (More)
We study the asymptotic performance of approximate maximum likelihood estimators for state space models obtained via sequential Monte Carlo methods. The state space of the latent Markov chain and the parameter space are assumed to be compact. The approximate estimates are computed by, firstly, running possibly dependent particle filters on a fixed grid in the parameter space, yielding a pointwise approximation of the log-likelihood function. Secondly, extensions of this approximation to the whole parameter space are formed by means of piecewise constant functions or B-spline interpolation, and approximate maximum likelihood estimates are obtained through maximization of the resulting functions. In this setting we formulate criteria for how to increase the number of particles and the resolution of the grid in order to produce estimates that are consistent and asymptotically normal. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
sequential Monte Carlo methods, consistency, asymptotic normality, hidden Markov model, maximum, particle filter, likelihood, state, space models
in
Stochastic Processes and their Applications
volume
118
issue
4
pages
649 - 680
publisher
Elsevier
external identifiers
  • wos:000254443200006
  • scopus:39149122537
ISSN
1879-209X
DOI
10.1016/j.spa.2007.05.007
language
English
LU publication?
yes
id
5070a913-a898-4112-90f3-f1cfa7785592 (old id 1182784)
date added to LUP
2008-09-01 16:10:46
date last changed
2017-01-01 06:25:32
@article{5070a913-a898-4112-90f3-f1cfa7785592,
  abstract     = {We study the asymptotic performance of approximate maximum likelihood estimators for state space models obtained via sequential Monte Carlo methods. The state space of the latent Markov chain and the parameter space are assumed to be compact. The approximate estimates are computed by, firstly, running possibly dependent particle filters on a fixed grid in the parameter space, yielding a pointwise approximation of the log-likelihood function. Secondly, extensions of this approximation to the whole parameter space are formed by means of piecewise constant functions or B-spline interpolation, and approximate maximum likelihood estimates are obtained through maximization of the resulting functions. In this setting we formulate criteria for how to increase the number of particles and the resolution of the grid in order to produce estimates that are consistent and asymptotically normal.},
  author       = {Olsson, Jimmy and Rydén, Tobias},
  issn         = {1879-209X},
  keyword      = {sequential Monte Carlo methods,consistency,asymptotic normality,hidden Markov model,maximum,particle filter,likelihood,state,space models},
  language     = {eng},
  number       = {4},
  pages        = {649--680},
  publisher    = {Elsevier},
  series       = {Stochastic Processes and their Applications},
  title        = {Asymptotic properties of particle filter-based maximum likelihood estimators for state space models},
  url          = {http://dx.doi.org/10.1016/j.spa.2007.05.007},
  volume       = {118},
  year         = {2008},
}