HISAPS: High-order smoothing spline with automatic parameter selection and shape constraints

Abstract

Obtaining a good functional fit with noisy data is difficult. This is especially true when the derivative of the fitted function is needed, which is often the case in engineering applications. One solution is to use smoothing splines. However, most conventional and readily available smoothing spline software implementations are cubic with a penalty on the 2nd order derivative, which results in poor and sometimes noisy derivatives. In this paper, we present new software that can be used to make smoothing splines with a penalty on the 1st, 2nd, 3rd, or 4th order derivatives. Furthermore, the presented software allows for applying constraints to the function to impose prior knowledge, including automatic parameter selection through cross-validation for an optimum and user-independent fit.