Some characteristics on the selection of spline smoothing parameter

ABSTRACT

The smoothing spline method is used to fit a curve to a noisy data set, where selection of the smoothing parameter is essential. An adaptive C_p criterion (Chen and Huang 2011) based on the Stein’s unbiased risk estimate has been proposed to select the smoothing parameter, which not only considers the usual effective degrees of freedom but also takes into account the selection variability. The resulting fitted curve has been shown to be superior and more stable than commonly used selection criteria and possesses the same asymptotic optimality as C_p. In this paper, we further discuss some characteristics on the selection of smoothing parameter, especially for the selection variability.

KEYWORDS:

• Non parametric regression
• selection variability
• smoothing spline
• Stein’s unbiased risk estimate

Acknowledgments

We would like to thank the editor, the associate editor, and the anonymous referee for helpful comments and suggestions.