Tore Selland Kleppe:Bandwidth Selection In Pre-Smoothed Particle Filters

Tore Selland Kleppe (University of Stavanger) gives a seminar in room 107, 1st floor N.H. Abels House at 14:15 November 11th: Bandwidth Selection In Pre-Smoothed Particle Filters

Abstract:
For the purpose of maximum likelihood estimation of static parameters,
we apply a kernel smoother to the particles in the standard SIR filter
for non-linear state space models with additive Gaussian observation
noise. This reduces the Monte Carlo error in the estimates of both
the posterior density of the states and the marginal density of the
observation at each time point. We correct for variance inflation
in the smoother, which together with the use of Gaussian kernels,
results in a Gaussian (Kalman) update when the amount of smoothing
turns to infinity. Our main contribution is a study of different criteria
for choosing the optimal bandwidth $h$ in the kernel smoother. We
derive the rate at which $h\rightarrow0$ as the number of particles
increases. The resulting formula is used to show consistency of posterior
and marginal densities. Finally, we illustrate our approach using
examples from econometrics. Our filter is shown to be highly suited
for dynamic models with high signal-to-noise ratio, for which the
SIR filter has problems.

 

Published Oct. 23, 2014 3:39 PM - Last modified Oct. 23, 2014 3:39 PM