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Article Dans Une Revue Probability and Mathematical Statistics Année : 2009

Optimality of the auxiliary particle filter

Résumé

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.
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Dates et versions

hal-00471534 , version 1 (08-04-2010)

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  • HAL Id : hal-00471534 , version 1

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Randal Douc, Éric Moulines, Jimmy Olsson. Optimality of the auxiliary particle filter. Probability and Mathematical Statistics, 2009, 29 (1), pp.1-28. ⟨hal-00471534⟩
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