Naive Penalized Spline Derivative Estimators Achieve Optimal Rates of Convergence

While it is common to study mean regression functions in statistical learning, there are many cases in economics, ecology, and nonparametric regression where it is of interest to estimate derivatives of the mean regression function with minimal assumptions on the functional form of the mean function. In this talk, I will discuss some theoretical findings for derivative estimation using nonparametric methods. In particular, we show that simply differentiating a penalized spline estimator of the mean regression function to estimate the corresponding derivative, achieves the optimal L2 rate of convergence.