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On Convergence of Kernel Density Estimates in Particle Filtering

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    0469752 - ÚI 2017 RIV CZ eng J - Journal Article
    Coufal, David
    On Convergence of Kernel Density Estimates in Particle Filtering.
    Kybernetika. Roč. 52, č. 5 (2016), s. 735-756. ISSN 0023-5954
    Grant - others: GA ČR(CZ) GA16-03708S; SVV(CZ) 260334/2016
    Institutional support: RVO:67985807
    Keywords : Fourier analysis * kernel methods * particle filter
    Subject RIV: BB - Applied Statistics, Operational Research
    Impact factor: 0.379, year: 2016

    The paper deals with kernel density estimates of filtering densities in the particle filter. The convergence of the estimates is investigated by means of Fourier analysis. It is shown that the estimates converge to the theoretical filtering densities in the mean integrated squared error. An upper bound on the convergence rate is given. The result is provided under a certain assumption on the Sobolev character of the filtering densities. A sufficient condition is presented for the persistence of this Sobolev character over time.
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