Optimal designs for trigonometric regression models

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• 作者：Holger Dette ; Viatcheslav B. Melas ; Petr Shpilev
• 关键词：L-optimal designs ; Fourier regression models ; Parameter subsets ; Equivalence theorem
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2011
• 出版时间：March 2011
• 年：2011
• 卷：141
• 期：3
• 页码：1343-1353
• 全文大小：271 K

文摘

In the common Fourier regression model we investigate the optimal design problem for the estimation of linear combinations of the coefficients, where the explanatory variable varies in the interval [−π,π]. In a recent paper Dette et al. (2009) determined optimal designs for estimating certain pairs of the coefficients in the model. The optimal design problem corresponds to a linear optimality criterion for a specific matrix L. In the present paper these results are extended to more general matrices L. By our results the optimal design problem for a Fourier regression of large degree can be reduced to a design problem in a model of lower degree, which allows the determination of L-optimal designs in many important cases. The results are illustrated by several examples.