A study of uniformity pattern for extended designs |
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| Authors: | Tingxun Gou Kashinath Chatterjee |
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| Institution: | 1. School of Mathematics and Statistics, Central China Normal University, Wuhan, China;2. Department of Statistics, Visva-Bharati University, Santiniketan, India |
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| Abstract: | The objective of this paper is to investigate the issue of projection discrepancy for extended U-type or nearly U-type extended designs along the line of Fang and Qin (2005 Fang, K. T., and H. Qin. 2005. Uniformity pattern and related criteria for two-level factorials. Science China Series A 48:1–11.Crossref] , Google Scholar]) based on the centered L2-discrepancy proposed in Hickernell (1998 Hickernell, F. J. 1998. A generalized discrepancy and quadrature error bound. Mathematics of Computation 67:299–322.Crossref], Web of Science ®] , Google Scholar]). Extended designs are obtained through augmenting optimally few runs (or points) to an optimal U-type design. Lower bounds to projection discrepancy with reference to the centered L2-discrepancy of extended designs have been obtained. Some illustrative examples are also provided. |
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| Keywords: | Centered L2-discrepancy lower bound projection discrepancy two-level uniform design |
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