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C. Rieser, P. Filzmoser:
"Piecewise smoothing splines";
Talk: ÖSG Statistiktage, Wien; 2019-10-24 - 2019-10-25.

Smoothing splines, as developed by Reinsch (1967), and their extension to GAMs, e.g. Wood(2017), are nowadays an indispensable tool in the modern days statistician´s toolbox. They havebeen used with great success in a variety of areas and continue to this day to be a very activefield of research. A survey carried out by Perperoglou et al. (2019) has shown that some splinepackages have been downloaded over 600.000 times.This great success of smoothing splines is due to the fact that often the relationship betweenthe response variableyand the predictorxcan be assumed to be smooth. However, if theground truth is not smooth over the whole range and contains jumps, this assumption is not ful-filled and leads to an estimate experiencing the so called Gibbs phenomenon, see Richards (1991).The presented method is considering a new approach which takes into account jumps inthe data. It is based on the assumption that the data can be modelled as piecewise smoothfunctions. Finding the breakpoints for these piecewise smooth functions is done in an non-iterative manner. By considering a penalized optimization problem we find multiple jumpsat once, in a computational feasible time. Our approach has the advantage that the class offunctions which it is able to approximate accurately exceeds the smoothing spline function class.