Statistica Sinica 14(2004), 591-601

CRITERION-ROBUST OPTIMAL DESIGNS FOR MODEL

DISCRIMINATION AND PARAMETER ESTIMATION:

MULTIVARIATE POLYNOMIAL REGRESSION CASE

Min-Hsiao Tsai and Mei-Mei Zen

National Cheng-Kung University

Abstract: Consider the problem of discriminating between two polynomial regression models on the $q$-cube $[-1,1]^{q}$, $q\ge{2}$, and estimating parameters in the models. To find designs which are efficient for both model discrimination and parameter estimation, Zen and Tsai (2002) proposed a multiple-objective optimality criterion for the univariate case. In this work, taking the same $M_{\gamma}$-criterion which uses weight $\gamma\;(0\le\gamma\le{1})$ for model discrimination and $1-\gamma$ for parameter estimation, the corresponding $M_{\gamma}$-optimal product design is investigated. Based on the maximin principle on the $M_{\gamma}$-efficiency of any $M_{\gamma'}$-optimal product design, a criterion-robust optimal product design is proposed.

Key words and phrases: Efficiency, γ-criterion, multiple-objective, product design.