An optimal control variance reduction method for density estimation

Ahmed Kebaier and Arturo Kohatsu-Higa

Stochastic Processes and their Applications, 2008, vol. 118, issue 12, 2143-2180

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.

Keywords: Kernel; density; estimation; Stochastic; differential; equations; Variance; reduction; Weak; approximation; Central; limit; theorem; Malliavin; calculus (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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