Automatic Smoothing for Discontinuous Regression Functions

This article proposes an automatic smoothing method for recovering discontinuous regression functions. The method models the target regression function with a series of disconnected cubic regression splines which partition the function’s domain. In this way discontinuity points can be incorporated in a fitted curve simply as the boundary points between adjacent splines. Three objective criteria are constructed and compared for choosing the number and placement of these discontinuity points as well as the amount of smoothing. These criteria are derived from three fundamentally different model selection methods: AIC, GCV and the MDL principle. Practical optimization of these criteria is done by genetic algorithms. Simulation results show that the proposed method is superior to many existing smoothing methods when the target function is non-smooth. The method is further made robust by using a Gaussian mixture approach to model outliers.