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Randomization of Quasi-Monte Carlo Methods for Error Estimation: Survey and Normal Approximation

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  • Tuffin Bruno

Abstract

Monte Carlo and quasi-Monte Carlo methods are simulation techniques that have been designed to efficiently estimate integrals for instance. Quasi-Monte Carlo asymptotically outperforms Monte Carlo, but the error can hardly be estimated. We propose here to recall how hybrid Monte Carlo/Quasi-Monte Carlo have been developed to easily get error estimations, with a special emphasis on the so-called randomly shifted low discrepancy sequences. Two additional points are investigated: we illustrate that the convergence rate is not always improved with respect to Monte Carlo and we discuss the confidence interval coverage problem.

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  • Tuffin Bruno, 2004. "Randomization of Quasi-Monte Carlo Methods for Error Estimation: Survey and Normal Approximation," Monte Carlo Methods and Applications, De Gruyter, vol. 10(3-4), pages 617-628.
    • Handle: RePEc:bpj:mcmeap:v:10:y:2004:i:3-4:p:617-628:n:1042
    DOI: 10.1515/mcma.2004.10.3-4.617
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