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October 2003 Optimal designs for estimating individual coefficients in Fourier regression models
Holger Dette, Viatcheslav B. Melas
Ann. Statist. 31(5): 1669-1692 (October 2003). DOI: 10.1214/aos/1065705122

Abstract

In the common trigonometric regression model, we investigate the optimal design problem for the estimation of the individual coefficients, where the explanatory variable varies in the interval $[-a,a]$, $0 <a \le \pi$. It is demonstrated that the structure of the optimal design depends sensitively on the size of the design space. For many important cases, optimal designs can be found explicitly, where the complexity of the solution depends on the value of the parameter a and the order of the term, for which the corresponding coefficient has to be estimated. The main tool of our approach is the reduction of the problem for the trigonometric regression model to a design problem for a polynomial regression. In particular, we determine the optimal designs for estimating the parameters corresponding to the cosine terms explicitly, if the design space is sufficiently small, and prove that under this condition all optimal designs for estimating the parameters corresponding to the sine terms are supported at the same points.

Citation

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Holger Dette. Viatcheslav B. Melas. "Optimal designs for estimating individual coefficients in Fourier regression models." Ann. Statist. 31 (5) 1669 - 1692, October 2003. https://doi.org/10.1214/aos/1065705122

Information

Published: October 2003
First available in Project Euclid: 9 October 2003

zbMATH: 1046.62076
MathSciNet: MR2012829
Digital Object Identifier: 10.1214/aos/1065705122

Subjects:
Primary: 62K05

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 5 • October 2003
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