On derivative estimation in spline regression

We consider the problem of estimating the derivatives of a regression funct ion by the corresponding derivatives of regression splines. Unlike kernel s moothers, these spline derivative estimators do not have boundary problems. In addition, they have simple expressions and are easy to compute. In this paper, me study the local asymptotic properties of these derivative estima tors. Under regularity conditions, the asymptotic bias and variance of thes e estimators are derived, and asymptotic normality is established. Furtherm ore, we extend the results to random designs and heteroscedastic errors.