Derivatives diagnostics and robustness for smoothing splines
Diagnostic measures for nonparametric regression using splines are given. Those measures which incorporate important information provided by the derivatives of the fitted curve have the potential of identifying different types of influential observations. These influential observations can substantially influence the spline fit. A robust nonparametric procedure can thus be developed by downweighting these influential observations. Numerical example and simulation results illustrate the techniques. Several applications are also given for a variety of nonparametric regression models.
robustness smoothing splines influential observations generalized cross-validation penalized likelihood regression diagnostics