Centered L<sub>2</sub>-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs - Research portal of Justus Liebig University Giessen:

Journal article

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

Authors list: Fang, KT; Ma, CX; Winker, P

Publication year: 2002

Pages: 275-296

Journal: Mathematics of Computation

Volume number: 71

Issue number: 237

ISSN: 0025-5718

DOI Link: https://doi.org/10.1090/S0025-5718-00-01281-3

Publisher: American Mathematical Society

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.

Authors/Editors

- Uni.-Prof. Dr. Peter Winker

Citation Styles

Harvard Citation style: Fang, K., Ma, C. and Winker, P. (2002) Centered L₂-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs, Mathematics of Computation, 71(237), pp. 275-296. https://doi.org/10.1090/S0025-5718-00-01281-3

APA Citation style: Fang, K., Ma, C., & Winker, P. (2002). Centered L₂-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs. Mathematics of Computation. 71(237), 275-296. https://doi.org/10.1090/S0025-5718-00-01281-3