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Optimal design for smoothing splines

Dette, H., Melas, V. B. and Pepelyshev, Andrey 2011. Optimal design for smoothing splines. Annals of the Institute of Statistical Mathematics 63 (5) , pp. 981-1003. 10.1007/s10463-009-0265-x

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Abstract

In the common nonparametric regression model we consider the problem of constructing optimal designs, if the unknown curve is estimated by a smoothing spline. A special basis for the space of natural splines is introduced and the local minimax property for these splines is used to derive two optimality criteria for the construction of optimal designs. The first criterion determines the design for a most precise estimation of the coefficients in the spline representation and corresponds to D-optimality, while the second criterion is the G-optimality criterion and corresponds to an accurate prediction of the curve. Several properties of the optimal designs are derived. In general, D- and G-optimal designs are not equivalent. Optimal designs are determined numerically and compared with the uniform design.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Smoothing spline; D- and G-optimal designs; Saturated designs
Publisher: Springer
ISSN: 0020-3157
Last Modified: 04 Jun 2017 05:09
URI: http://orca.cf.ac.uk/id/eprint/49066

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