A Lower Bound for the Centered L2-Discrepancy on Asymmetric Factorials and its Application |
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| Authors: | Kashinath?Chatterjee,Kai-Tai?Fang,Hong?Qin mailto:qinhong@mail.ccnu.edu.cn" title=" qinhong@mail.ccnu.edu.cn" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author |
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| Affiliation: | (1) Department of Statistics, Visva-Bharati University, Santiniketan, India;(2) Department of Mathematics, Hong Kong Baptist University, Hong Kong, China;(3) Department of Statistics, Central China Normal University, Wuhan, 430079, China |
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| Abstract: | ![]()
The role of uniformity measured by the centered L 2-discrepancy (Hickernell 1998a) has been studied in fractional factorial designs. The issue of a lower bound for the centered L 2-discrepancy is crucial in the construction of uniform designs. Fang and Mukerjee (2000) and Fang et al. (2002, 2003b) derived lower bounds for fractions of two- and three-level factorials. In this paper we report some new lower bounds for the centered L 2-discrepancy for a set of asymmetric fraction factorials. Using these lower bounds helps to measure uniformity of a given design. In addition, as an application of these lower bounds, we propose a method to construct uniform designs or nearly uniform designs with asymmetric factorials. |
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| Keywords: | Asymmetric factorial Centered L 2-discrepancy Uniformity Uniform design |
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