AISM 53, 418-426
© 2001 ISM

A new design criterion when heteroscedasticity is ignored

Grace Montepiedra1 and Weng Kee Wong2

1Department of Applied Statistics and Operations Research, Bowling Green State University, Bowling Green, OH 43403, U.S.A.
2Department of Biostatistics, UCLA, 10833 Le Conte Ave, Los Angeles, CA 90095-1772, U.S.A.

(Received July 21, 1998; revised August 17, 1999)

Abstract.    This paper examines the construction of optimal designs when one assumes a homoscedastic linear model, but the underlying model is heteroscedastic. A criterion that takes this type of misspecification into account is formulated and an equivalence theorem is given. We also provide explicit optimal designs for single-factor and multi-factor experiments under various heteroscedastic assumptions and discuss the relationship between the D-optimal design sought here and the conventional D-optimal design.

Key words and phrases:    Heteroscedasticity, D-optimal, efficiency function, equivalence theorem, mean squared error, L-optimal, multi-factor experiment.

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