Robust Fitting of Discontinuous Regression Functions

Keywords: discontinuity-preserving, genetic algorithm, minimum description length, robust curve fitting

Abstract: An automatic and robust regression procedure that is capable of recovering curves with discontinuity points from noisy observations is developed. In this procedure unknown functions are modelled by series of disjoint cubic regression splines, discontinuity points are assumed to be located at junctions between adjacent splines, and "normal noise" and outliers are separated by a Gaussian-mixture based technique. The "best" curve estimate is chosen by the minimum description length principle, and a genetic algorithm is developed for numerically obtaining this "best" estimate. Simulation results suggest that the proposed procedure is very promising.