Abstract.
Smoothing spline estimation of a function of several variables based on an analysis of variance decomposition (SS-ANOVA) is one modern nonparametric technique. This paper considers the design problem for specific types of SS-ANOVA models. As criteria for choosing the design points, the integrated mean squared error (IMSE) for the SS-ANOVA estimate and its asymptotic approximation are derived based on the correspondence between the SS-ANOVA model and the random effects model with a partially improper prior. Three examples for additive and interaction spline models are provided for illustration. A comparison of the asymptotic designs, the 2d factorial designs, and the glp designs is given by numerical computation.
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Received May 2000
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Yue, RX., Hickernell, F. Designs for smoothing spline ANOVA models. Metrika 55, 161–176 (2002). https://doi.org/10.1007/s001840100136
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DOI: https://doi.org/10.1007/s001840100136