Smoothing splines with variable continuity properties and degree

Abstract

When using smoothing splines, a feature of the data, for example, a sharp turn, which we would like to retain is sometimes lost. If a smoothing spline with less than the usual order of continuity at the data points is fitted then we may retain this feature but at the cost of not smoothing out the parts of the data we want smoothed. The approach presented can retain a feature of the data while smoothing out the rest of the data by selectively reducing the continuity at some of the data points or the degree of the piecewise polynomial being fitted in some of the intervals. This approach is a development of the generalisation of the stochastic formulation of smoothing splines given in [1].