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Journal Articles Journal of Statistical Computation and Simulation Year : 2003

Reducing variance using iterated control variates

Sylvain Maire
• Function : Author

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.

Dates and versions

hal-01479850 , version 1 (28-02-2017)

Identifiers

• HAL Id : hal-01479850 , version 1
• DOI :

Cite

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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