Dette, Holger, Melas, V.B. and Biedermann, Stefanie
A functional-algebraic determination of D-optimal designs for trigonometric regression models on a partial circle.
Statistics & Probability Letters, 58, (4), . (doi:10.1016/S0167-7152(02)00152-9).
We investigate the D-optimal design problem in the common trigonometric regression model, where the design space is a partial circle. The task of maximizing the criterion function is transformed into the problem of determining an eigenvalue of a certain matrix via a differential equation approach. Since this eigenvalue is an analytic function of the length of the design space, we can make use of a Taylor expansion to provide a recursive algorithm for its calculation. Finally, this enables us to determine Taylor expansions for the support points of the D-optimal design.
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