Optimal and Robust Designs for Full and Reduced Fourier Regression Models

Abstract

The optimal and robust designs for Fourier regression models under different optimality criteria are discussed. First, we discuss the classical Q‐optimal designs for estimating the response function in a full Fourier regression model with a given order. Second, we investigate the minimax designs in case of Fourier approximation under A‐, D‐, and Q‐optimality. We also demonstrate the equivalency of Q‐optimal and A‐optimal designs for Fourier regression in general. Third, the insensitivity of our resulting designs to a misspecified order of an assumed model is also discussed. Last, the D‐optimal designs for some useful reduced Fourier models are constructed. The comparison study shows that the constructed designs incorporating the reduced models are efficient.