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

Monte Carlo and quasi Monte Carlo methods are simulation techniques that have been de signed to e ciently 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 em phasis 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 con dence interval coverage problem