Eric Moulines, Paris

Title: On the auxiliary particle filter

In this article we study asymptotic properties of weighted samples
produced by the two-stage sampling (TSS) particle filter, which is a
generalization of the auxiliary particle filter proposed by Pitt and
Shephard (1999). Besides establishing a central limit theorem (CLT) for
smoothed particle estimates, we also derive bounds on the Lp error and bias
of the same for a finite particle sample size. By examining the recursive
formula for the asymptotic variance of the CLT we identify first-stage
importance weights for which the increase of asymptotic variance at a single
iteration of the algorithm is minimal. Finally, we discuss how these weights
can be used for evaluating the performance of the TSS method in relation to
standard sequential Monte Carlo methods and suggest, in the light of our
findings, some possible improvements of the TSS algorithm.