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Enhanced consistency of the Resampled Convolution Particle Filter

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  • Vila, Jean-Pierre
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    Abstract

    Among the convolution particle filters for discrete-time dynamic systems defined by nonlinear state space models, the Resampled Convolution Filter is one of the most efficient, in terms of estimation of the conditional probability density functions (pdf’s) of the state variables and unknown parameters and in terms of implementation. This nonparametric filter is known for its almost sure L1-convergence property. But contrarily to the other convolution filters, its almost sure punctual convergence had not yet been established. This paper is devoted to the proof of this property.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 4 ()
    Pages: 786-797

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:786-797

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    Related research

    Keywords: State space dynamic systems; Particle filtering; Kernel density estimator; Resampled Convolution Filter;

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    1. LeGland, François & Oudjane, Nadia, 2003. "A robustification approach to stability and to uniform particle approximation of nonlinear filters: the example of pseudo-mixing signals," Stochastic Processes and their Applications, Elsevier, vol. 106(2), pages 279-316, August.
    2. Vila, Jean-Pierre, 2011. "Nonparametric multi-step prediction in nonlinear state space dynamic systems," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 71-76, January.
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