A NEW DESIGN CRITERION WHEN HETEROSCEDASTICITY IS IGNORED

GRACE MONTEPIEDRA^{1}, AND WENG KEE WONG^{2}

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 singlefactor 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.