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Reducing variance using iterated control variates

Sylvain Maire 1, 2 
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : In this paper we describe a new variance reduction method for Monte Carlo integration based on an iterated computation of $L^2$ approximations using control variates. This computation leads to non linear unbiased estimates for each of the coefficients of the truncated $L^2$ expansion. We give estimations of the variance of these estimates without further hypotheses on the approximation basis. We study especially the convergence of our algorithm in the case of a polynomial decay of these coefficients. As an application, regular monodimensional functions will be approximated using a Fourier basis on periodised functions, Legendre and Tchebychef polynomial $L^2$ approximations. The order of our method will appear to be almost optimal in this case. Numerical examples will be given as a comparison with standard Monte Carlo estimates.
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Submitted on : Tuesday, February 28, 2017 - 10:25:14 PM
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Sylvain Maire. Reducing variance using iterated control variates. Journal of Statistical Computation and Simulation, 2003, 73 (1), pp.1-30. ⟨10.1080/00949650215726⟩. ⟨hal-01479850⟩



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