A Non-iterative Optimization for Smoothness in Penalized Spline Regression

Typically, an optimal smoothing parameter in a penalized spline regression is determined by minimizing an information criterion, such as one of the Cp, CV and GCV criteria. Since an explicit solution to the minimization problem for an information criterion cannot be obtained, it is necessary to carry out an iterative procedure to search for the optimal smoothing parameter, i.e., a grid search method. In order to avoid such extra calculation, a non-iterative optimization method for smoothness in penalized spline regression is proposed using the formulation of generalized ridge regression. By conducting numerical simulations, we verify that our method has better performance than other methods which optimize the number of basis functions and the single smoothing parameter by means of the CV or GCV criteria. MSC 2010 subject classifications: Primary 62G08; Secondary 62J07.