Minimum bias designs with constraints |
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| Affiliation: | 1. UTBM – Université de Technologie Belfort-Montbéliard, ICB-COMM, CNRS UMR 6303, Sevenans, France;2. Ecole Centrale de Nantes, LS2N, CNRS UMR 6004, Nantes, France;3. MINES ParisTech, PSL - Research University, CEMEF - Centre de Mise en Forme des Matériaux, CNRS UMR 7635, Sophia Antipolis Cedex, France;1. University of New South Wales, Sydney, NSW 2052, Australia;2. Swiss Federal Institute of Technology Lausanne, Rte Cantonale, 1015 Lausanne, Switzerland;1. Center for Biostatistics in AIDS Research and Department of Biostatistics, Harvard T.H. Chan School of Public Health, 677 Huntington Avenue, Boston, MA 02115, USAn;2. Division of Global Health Equity, Brigham and Women''s Hospital, 75 Francis Street, Boston, MA 02115, USA |
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| Abstract: | A new class of model-robust optimality criteria, based on the mean squared error, is introduced in this paper. 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 Box and Draper (1959, J. Amer. Statist. Assoc. 54, 622–654), 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. |
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