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Enhanced consistency of the Resampled Convolution Particle Filter

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  • Vila, Jean-Pierre

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.

Suggested Citation

  • Vila, Jean-Pierre, 2012. "Enhanced consistency of the Resampled Convolution Particle Filter," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 786-797.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:786-797
    DOI: 10.1016/j.spl.2012.01.003
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    References listed on IDEAS

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    1. 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.
    2. Gimenez, Olivier & Rossi, Vivien & Choquet, Rémi & Dehais, Camille & Doris, Blaise & Varella, Hubert & Vila, Jean-Pierre & Pradel, Roger, 2007. "State-space modelling of data on marked individuals," Ecological Modelling, Elsevier, vol. 206(3), pages 431-438.
    3. 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.
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