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

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.