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Contents of PMS, Vol. 29, Fasc. 1,
pages 1 - 28
 

OPTIMALITY OF THE AUXILIARY PARTICLE FILTER

Randal Douc
Éric Moulines
Jimmy Olsson

Abstract: In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by Pitt and Shephard [17]. 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. In the light of these findings, we discuss and demonstrate on several examples how the APF algorithm can be improved.

2000 AMS Mathematics Subject Classification: Primary: 65C05; Secondary: 65C60.

Keywords and phrases: Auxiliary particle filter, central limit theorem, adjustment multiplier weight, sequential Monte Carlo, state space model, stratified sampling, two-stage sampling.

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