Abstract
Uniformity has played a key role in quasi-Monte Carlo methods as well as in computer experiments. The minimum aberration is the most popular criterion in factorial designs. In this paper we extend the results of Fang and Mukerjee (2000) from regular fractions of two-level factorials to regular fractions 3s-1 of three-level factorials and establish a relationship between uniformity and aberration of regular fractions 3s-1. There are many minimum aberration fractions 3s-1 whose performances in statistical estimation may be different even though they are isomorphic to each other. Uniformity can be used as a criterion for comparing designs. A new concept of uniformly regular design is proposed. Construction of uniformly regular 3s-1 designs is studied. We show that the uniformly minimum aberration 3s-1 design has lower correlation and less confounding than the non-uniform one.
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© 2002 Springer-Verlag Berlin Heidelberg
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Fang, KT., Ma, CX. (2002). Relationships Between Uniformity, Aberration and Correlation in Regular Fractions 3s-1 . In: Fang, KT., Niederreiter, H., Hickernell, F.J. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56046-0_14
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DOI: https://doi.org/10.1007/978-3-642-56046-0_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42718-6
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