$T$-optimal discriminating designs for Fourier regression models

TL;DR

This paper develops explicit solutions for constructing $T$-optimal discriminating designs in Fourier regression models, especially when models differ by up to three trigonometric functions, and explores their dependence on model parameters.

Contribution

It provides analytical solutions for $T$-optimal designs in specific Fourier models and investigates their parameter dependence both analytically and numerically.

Findings

Explicit solutions for models differing by up to three functions.

Numerical analysis of $T$-optimal design dependence on parameters.

Low efficiency of $D$- and $D_s$-optimal designs for $T$-optimality.

Abstract

In this paper we consider the problem of constructing $T$-optimal discriminating designs for Fourier regression models. We provide explicit solutions of the optimal design problem for discriminating between two Fourier regression models, which differ by at most three trigonometric functions. In general, the $T$-optimal discriminating design depends in a complicated way on the parameters of the larger model, and for special configurations of the parameters $T$-optimal discriminating designs can be found analytically. Moreover, we also study this dependence in the remaining cases by calculating the optimal designs numerically. In particular, it is demonstrated that $D$- and $D_s$-optimal designs have rather low efficiencies with respect to the $T$-optimality criterion.