On the auxiliary particle filter

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In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) 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. In the light of these findings, we discuss and demonstrate on several examples how the APF algorithm can be improved.
26 pages

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Statistics Theory, Primary 65C05; Secondary 65C60

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http://salesiana.dossiersoluciones.com/handle/123456789/138522

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0709.3448
 http://arxiv.org/abs/0709.3448

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arXiv