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Biometrika 2002 89(4):893-904; doi:10.1093/biomet/89.4.893
© 2002 by Biometrika Trust
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Uniform designs limit aliasing

Fred J.Hickernell1 and Min-Qian Liu2

1 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China fred{at}hkbu.edu.hk 2 School of Management, Tianjin University, Tianjin 300072, China mqliu{at}263.net

When fitting a linear regression model to data, aliasing can adversely affect the estimates of the model coefficients and the decision of whether or not a term is significant.Optimal experimental designs give efficient estimators assuming that the true form of the model is known, while robust experimental designs guard against inaccurate estimates caused by model misspecification. Although it is rare for a single design to be both maximally efficient and robust, it is shown here that uniform designs limit the effects of aliasing to yield reasonable efficiency and robustness together. Aberration and resolution measure how well fractional factorial designs guard against the effects of aliasing. Here it is shown that the definitions of aberration and resolution may be generalised to other types of design using the discrepancy.

Key Words: Discrepancy; Effects aliasing; Fractional factorial design; Minimum aberration; Orthogonal array; Reproducing kernel Hilbert space; Resolution

Received January 2001. Revised April 2002


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