Wrap-Around L2-Discrepancy of Random Sampling, Latin Hypercube and Uniform Designs

Centered L2-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs

In this paper properties and construction of designs under a centered version of the L2-discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is als...

Lower bounds for wrap-around L2-discrepancy and constructions of symmetrical uniform designs

The wrap-around L2-discrepancy has been used in quasi-Monte Carlo methods, especially in experimental designs. In this paper, explicit lower bounds of the wrap-aroundL2-discrepancy of U-type designs are obtained. Sufficient conditions for U-type designs to achieve their lower bounds are given. Taking advantage of these conditions, we consider the perfect resolvable balanced incomplete block des...

Nested Latin hypercube designs

We propose an approach to constructing nested Latin hypercube designs. Such designs are useful for conducting multiple computer experiments with different levels of accuracy. A nested Latin hypercube design with two layers is defined to be a special Latin hypercube design that contains a smaller Latin hypercube design as a subset. Our method is easy to implement and can accommodate any number o...

Sliced Latin Hypercube Designs

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2 the Wd of Random Sampling and Latin Hypercube