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Minimum bias designs with constraints. (English) Zbl 0899.62096
Summary: A new class of model-robust optimality criteria, based on the mean squared error, is introduced. The motivation is to find designs when the researcher is more concerned with controlling the variance than the bias, or vice versa. The set of criteria proposed here is also appealing from a mathematical perspective in the sense that, unlike the G. E. P. Box and N. R. Draper [J. Am. Stat. Assoc. 54, 622-654 (1959; Zbl 0116.36804)] criterion, they can be imbedded in the framework of convex design theory and, hence, facilitate the search for globally optimal designs. The basic idea is to minimize a convex function of the bias part of the mean squared error subject to a convex constraint on the variance part, or vice versa. Equivalence theorems are derived and examples for the linear and quadratic regression problems are provided.

MSC:
62K05 Optimal statistical designs
90C25 Convex programming
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