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

Tuffin Bruno

Monte Carlo Methods and Applications, 2004, vol. 10, issue 3-4, 617-628

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.

Date: 2004
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DOI: 10.1515/mcma.2004.10.3-4.617

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