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Abstract:
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In penalized spline regression, it is important to select an appropriate smoothing parameter. We often determine the optimal smoothing parameter by the minimizer of the cross-validation, although it is usually obtained by the computational grid selection. In this paper, we investigate asymptotic properties of the cross-validation and then show that the optimal smoothing parameter can be obtained in a closed form by neglecting the higher-order terms. The closed form can also illustrate an empirically known behavior of the optimal smoothing parameter. Using the closed form, we propose a sequential selection of the smoothing parameter and compare its performance with the usual estimate and the grid selection. The sequential selection largely improve the usual estimate and is often comparable with the grid selection.
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