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Using discrepancy to evaluate fractional factorial designs. (English) Zbl 0994.62074

Fang, Kai-Tai (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 2000. Proceedings of a conference, held at Hong Kong Baptist Univ., Hong Kong SAR, China, November 27 - December 1, 2000. Berlin: Springer. 357-368 (2002).
Summary: Fractional factorial design is arguably the most widely used design in experimental investigation, and uniformity has gained popularity in experimental designs in recent years. In this paper, a suitable measure of uniformity, i.e. a discrete discrepancy, is defined by the reproducing kernel Hilbert space, and is used to evaluate the uniformity of fractional factorial designs. Some relations between orthogonality and uniformity in fractional factorial designs are obtained. The results show that orthogonality and uniformity are strongly related to each other and the discrepancy plays an important role in evaluating such experimental designs.
For the entire collection see [Zbl 0980.00040].

MSC:

62K15 Factorial statistical designs
46N30 Applications of functional analysis in probability theory and statistics
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