Consider the problem of discriminating between two competitive Fourier regression on the circle [-π,π] 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 Mγ-criterion, which puts weight γ (0≤γ≤1) for model discrimination and 1-γ for parameter estimation, and using the techniques of projection design, the corresponding Mγ-optimal design for Fourier regression models is explicitly derived in terms of canonical moments. The behavior of the Mγ-optimal designs is investigated under different weighted selection criterion. And the extreme value of the minimum Mγ-efficiency of any Mγ′-optimal design is obtained at γ′=γ*, which results in the Mγ*-optimal design to be served as a criterion-robust optimal design for the problem.
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