A robust variant of cubic smoothing spline approximation

We introduce a robust variant of smoothing spline regression which exploits an entropy-based argument to automatically detect and remove outliers during the fitting procedure. This involves considering a penalized weighted residual sum of squares, with the distribution of weights determined by maximizing the associated entropy function. An illustrative example is provided to show the potential of the new approach compared to other standard robust techniques. Additionally, we include examples on datasets derived from real-world applications.