Some characteristics on the selection of spline smoothing parameter

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.