Randomly Permuted (t,m,s)-Nets and (t, s)-Sequences
This article presents a hybrid of Monte Carlo and Quasi-Monte Carlo methods. In this hybrid, certain low discrepancy point sets and sequences due to Faure, Niederreiter and Sobol’ are obtained and their digits are randomly permuted. Since this randomization preserves the equidistribution properties of the points it also preserves the proven bounds on their quadrature errors. The accuracy of an estimated integrand can be assessed by replication, consisting of independent re-randomizations.
KeywordsOrthogonal Array Latin Hypercube Sample Probability Zero Monte Carlo Variance Elementary Interval
Unable to display preview. Download preview PDF.
- Genz, A. (1984). Testing Multidimensional Integration Routines, in Tools, Methods and Languages for Scientific and Engineering Computation, B. Ford, J. C. Rault, & F. Thomasset, eds., 81 – 94 North-Holland, Amsterdam.Google Scholar
- Hall, P. (1992). The Bootstrap and Edgeworth Expansion. Springer, New York.Google Scholar
- Owen, A. B. (1990). Empirical Likelihood and Small Samples. Computing Science and Statistics, Proceedings of the 22nd Symposium on the Interface A.S.A., Alexandria VA.Google Scholar
- Owen, A. B. (1992a). A Central Limit Theorem for Latin Hypercube Sampling. Journal of the Royal Statistical Society, Ser. B. Google Scholar
- Owen, A.B. (1994b). “Monte Carlo Variance of Scrambled Equidistribution Quadrature”. Dept. of Statistics Technical Report Number 466, Stanford University.Google Scholar