A New Design Criterion When Heteroscedasticity is Ignored

Authors: Montepiedra G.¹; Wong W.K.²

Source: Annals of the Institute of Statistical Mathematics, Volume 53, Number 2, June 2001 , pp. 418-426(9)

Publisher: Springer

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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.

Keywords: Heteroscedasticity; D-optimal; efficiency function; equivalence theorem; mean squared error; L-optimal; multi-factor experiment

Language: English

Document Type: Regular paper

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

Publication date: 2001-06-01