Statistica Sinica 12(2002), 917-930

OPTIMAL DESIGNS FOR FIRST-ORDER TRIGONOMETRIC

REGRESSION ON A PARTIAL CYCLE

Huaiqing Wu

Iowa State University

Abstract: Trigonometric regression is commonly used to describe cyclic phenomena that occur in the engineering, biological, and medical sciences. Optimal designs for this model on a complete cycle have been studied extensively in the literature. However, much less attention has been paid to the design problem with a partial cycle. This paper solves this problem for the first-order trigonometric regression. Explicit $D$-, $A$-, and $E$-optimal designs are analytically derived. These designs are used to evaluate the $D$-, $A$-, and $E$-efficiencies of the equidistant sampling method commonly used in practice. Efficient and practical designs are then suggested. Some optimal exact designs and optimal designs for all nontrivial subsets of the coefficients are also obtained. A discussion is made on the $\phi_p$-optimal designs ( $p \in [-\infty, 1]$) for the general trigonometric regression on a partial cycle.

Key words and phrases: A-optimality, D-optimality, efficiency, E-optimality, equidistant sampling, exact design, Φp-criterion.