Asymptotic properties of the bootstrap particle filter maximum likelihood
estimator for state space models
Jimmy Olsson and Tobias Rydén
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2005
ISSN 14039338

Abstract:


We study the asymptotic performance of an approximatemaximum likelihood estimator
for state space models obtained via the bootstrap particle filter. The state
space of the latent Markov chain and the parameter space are assumed to be
compact. The approximate estimate is computed by, firstly, running possibly
dependent particle filters on a fixed grid in the parameter space, yielding
a pointwise approximation of the likelihood function. Secondly, the estimate
is obtained by maximizing this approximation over the grid. In this setting
we formulate criteria for how to increase the number of particles, and how
to vary the grid size in order to produce an estimate that is consistent
and asymptotically normal.



Key words:

Asymptotic normality, bootstrap particle filter, consistency, hidden Markov
model, maximum likelihood, sequential Monte Carlo methods, state space models.
