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Scrambling non-uniform nets

In: Mathematica Slovaca, vol. 59, no. 3
Shu Tezuka


Year, pages: 2009, 379 - 386
high-dimensional numerical integration, Latin hypercube sampling, Owen's scrambling, Sobol' points, $(t, m, d)$-nets
About article:
In this paper, we consider Owen's scrambling of an \mbox{$(m{-}1,m,d)$-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 $L2$ functions on $[0,1]d$. Second ly, 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.
How to cite:
ISO 690:
Tezuka, S. 2009. Scrambling non-uniform nets. In Mathematica Slovaca, vol. 59, no.3, pp. 379-386. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0134-3

Tezuka, S. (2009). Scrambling non-uniform nets. Mathematica Slovaca, 59(3), 379-386. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0134-3
About edition: