Criterion-robust optimal designs for model discrimination and parameter estimation in Fourier regression models

Consider the problem of discriminating between two competitive Fourier regression on the circle [-pi, pi] and estimating parameters in the models. To find designs which are efficient for both model discrimination and parameter estimation, Zen and Tsai (some criterion-robust optimal designs for the dual problem of model discrimination and parameter estimation, Indian J. Statist. 64, 322-338) proposed a multiple-objective optimality criterion for polynomial regression models. In this work, taking the same M-gamma-criterion, which puts weight gamma (0 less than or equal to gamma less than or equal to 1) for model discrimination and 1 - gamma for parameter estimation, and using the techniques of projection design, the corresponding M-gamma-optimal design for Fourier regression models is explicitly derived in terms of canonical moments. The behavior of the M-gamma-optimal designs is investigated under different weighted selection criterion. And the extreme value of the minimum M-gamma-efficiency of any M-gamma-optimal design is obtained at gamma' = gamma*, which results in the M-gamma*-optimal design to be served as a criterion-robust optimal design for the problem. (C) 2003 Elsevier B.V. All rights reserved.