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

Fang, Kai-Tai; Ma, Chang-Xing; Winker, Peter

doi:10.1090/S0025-5718-00-01281-3

Centered $L_2$-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs
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by Kai-Tai Fang, Chang-Xing Ma and Peter Winker PDF

Math. Comp. 71 (2002), 275-296 Request permission

Abstract:

In this paper properties and construction of designs under a centered version of the $L_2$-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 also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.

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