Asymptotic properties of particle filter-based maximum likelihood estimators for state space models
2008 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, Vol. 118, no 4, 649-680 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2008. Vol. 118, no 4, 649-680 p.
asymptotic normality; consistency; hidden Markov model; maximum likelihood; particle filter; sequential Monte Carlo methods; state space models
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-61481DOI: 10.1016/j.spa.2007.05.007ISI: 000254443200006OAI: oai:DiVA.org:kth-61481DiVA: diva2:479197
QC 201201252012-01-172012-01-172012-01-25Bibliographically approved