Naive Penalized Spline Estimators of Derivatives Achieve Optimal Rates of Convergence. (arXiv:2208.10664v1 [math.ST])

This paper studies the asymptotic behavior of penalized spline estimates of
derivatives. In particular, we show that simply differentiating the penalized
spline estimator of the mean regression function itself to estimate the
corresponding derivative achieves the optimal L2 rate of convergence.

arxiv convergence derivatives math spline