Statistica Sinica 19 (2009), 1587-1601

OPTIMAL DESIGNS FOR ESTIMATING PAIRS OF

COEFFICIENTS IN FOURIER REGRESSION MODELS

Holger Dette$^1$, Viatcheslav B. Melas$^2$ and Petr Shpilev$^2$

$^1$Ruhr-Universität Bochum and $^2$St. Petersburg State University

Abstract: In the common Fourier regression model we investigate the optimal design problem for estimating pairs of the coefficients, where the explanatory variable varies in the interval $[-\pi, \pi]$. $L$-optimal designs are considered and for many important cases $L$-optimal designs can be found explicitly, where the complexity of the solution depends on the degree of the trigonometric regression model and the order of the terms for which the pair of the coefficients has to be estimated.

Key words and phrases: Equivalence theorem, Fourier regression models, L-optimal designs, parameter subsets.