Parameter selection for smoothing splines using Stein's Unbiased Risk Estimator

Abstract

A challenging problem in smoothing spline regression is determining a value for the smoothing parameter. The parameter establishes the tradeoff between the closeness of the data, versus the smoothness of the regression function. This paper proposes a new method of finding the optimum smoothness value based on Stein's Unbiased Risk Estimator (SURE). This approach employs Newton's method to solve for the optimal value directly, while minimizing the true error of the regression. Experimental results demonstrate the effectiveness of this method, particularly for small datasets.