Some new lower bounds to various discrepancies on combined designs |
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| Authors: | Zujun Ou Kashinath Chatterjee |
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| Institution: | 1. College of Mathematics and Statistics, Jishou University, Jishou, China;2. College of Physical Science and Technology, Central China Normal University, Wuhan, China;3. Department of Statistics, Visva-Bharati University, Santiniketan, India |
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| Abstract: | The foldover is a useful technique in construction of two-level factorial designs. A foldover design is the follow-up experiment generated by reversing the sign(s) of one or more factors in the initial design. The full design obtained by joining the runs in the foldover design to those of the initial design is called the combined design. In this article, some new lower bounds of various discrepancies of combined designs, such as the centered, symmetric, and wrap-around L2-discrepancies, are obtained, which can be used as a better benchmark for searching optimal foldover plans. Our results provide a theoretical justification for optimal foldover plans in terms of uniformity criterion. |
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| Keywords: | Combined design Discrepancy Lower bound Optimal foldover plan Uniformity |
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