Affiliation:
1. Faculty of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku Fukuoka-shi, Fukuoka-ken, Japan, 812-8581
Abstract
Abstract
In this paper, we consider Owen’s scrambling of an (m−1, m, d)-net in base b which consists of d copies of a (0, m, 1)-net in base b, and derive an exact formula for the gain coefficients of these nets. This formula leads us to a necessary and sufficient condition for scrambled (m − 1, m, d)-nets to have smaller variance than simple Monte Carlo methods for the class of L
2 functions on [0, 1]d. Secondly, from the viewpoint of the Latin hypercube scrambling, we compare scrambled non-uniform nets with scrambled uniform nets. An important consequence is that in the case of base two, many more gain coefficients are equal to zero in scrambled (m − 1, m, d)-nets than in scrambled Sobol’ points for practical size of samples and dimensions.
Cited by
1 articles.
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