D-Optimal Designs for Trigonometric Regression Models on a Partial Circle

Authors: Dette H.¹; Melas V.B.²; Pepelyshev A.³

Source: Annals of the Institute of Statistical Mathematics, Volume 54, Number 4, 2002 , pp. 945-959(15)

Publisher: Springer

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Abstract:

In the common trigonometric regression model we investigate the D-optimal design problem, where the design space is a partial circle. It is demonstrated that the structure of the optimal design depends only on the length of the design space and that the support points (and weights) are analytic functions of this parameter. By means of a Taylor expansion we provide a recursive algorithm such that the D-optimal designs for Fourier regression models on a partial circle can be determined in all cases. In the linear and quadratic case the D-optimal design can be determined explicitly.

Keywords: Trigonometric regression; D-optimality; implicit function theorem; orthogonal polynomial

Language: English

Document Type: Research article

Affiliations: 1: Fakultät für Mathematik, Lehrstuhl III (Stochastik), Ruhr-Universität Bochum, Gebaude NA 3/72, 44780 Bochum, Germany, e-mail: holger.dette@ruhr-uni-bochum.de 2: Department of Mathematics, St. Petersburg State University, St. Petersburg, Russian Federation, e-mail: v.melas@pobox.spbu.ru 3: Department of Mathematics, St. Petersburg State University, St. Petersburg, Russian Federation, e-mail: andrey@ap7236.spb.edu

Publication date: 2002-01-01