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

摘要

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.