The statistical properties of a cubic smoothing spline and its derivative are analyzed. It is shown that unless unnatural boundary conditions hold, the integrated squared bias is dominated by local effects near the boundary. Similar effects are shown to occur in the regularized solution of a translation-kernel integral equation. These results are derived by developing a Fourier representation for a smoothing spline.
"Smoothing Splines: Regression, Derivatives and Deconvolution." Ann. Statist. 11 (1) 141 - 156, March, 1983. https://doi.org/10.1214/aos/1176346065