Randomization of quasi-Monte Carlo methods for error estimation: survey and normal approximation. (English) Zbl 1066.65011
Summary: 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.
MSC:
65C05 | Monte Carlo methods |