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An optimal control variance reduction method for density estimation

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  • Kebaier, Ahmed
  • Kohatsu-Higa, Arturo
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    Abstract

    We study the problem of density estimation of a non-degenerate diffusion using kernel functions. Thanks to Malliavin calculus techniques, we obtain an expansion of the discretization error. Then, we introduce a new control variate method in order to reduce the variance in the density estimation. We prove a stable law convergence theorem of the type obtained in Jacod-Kurtz-Protter for the first Malliavin derivative of the error process, which leads us to get a CLT for the new control variate algorithm. This CLT gives us a precise description of the optimal parameters of the method.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 118 (2008)
    Issue (Month): 12 (December)
    Pages: 2143-2180

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    Handle: RePEc:eee:spapps:v:118:y:2008:i:12:p:2143-2180

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    Related research

    Keywords: Kernel density estimation Stochastic differential equations Variance reduction Weak approximation Central limit theorem Malliavin calculus;

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    1. Arturo Kohatsu & Roger Pettersson, 2002. "Variance reduction methods for simulation of densities on Wiener space," Economics Working Papers 597, Department of Economics and Business, Universitat Pompeu Fabra.
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