Asymptotic properties of particle filter-based maximum likelihood estimators for state space models
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1182784
- author
- Olsson, Jimmy LU and Rydén, Tobias LU
- organization
- publishing date
- 2008
- 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
- 2016-04-01 14:46:06
- date last changed
- 2022-01-28 02:25:49
@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}},
keywords = {{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}},
doi = {{10.1016/j.spa.2007.05.007}},
volume = {{118}},
year = {{2008}},
}