Central limit theorems for the integrated squared error of derivative estimators

Abstract

A central limit theorem for the weighted integrated squared error of kernel type estimators of the first two derivatives of a nonparametric regression function is proved by using results for martingale differences and U-statistics. The results focus on the setting of the Nadaraya-Watson estimator but can also be transfered to local polynomial estimates. --central limit theorem,integrated squared error,kernel estimates,local polynomial estimate,Nadaraya-Watson estimate,nonparametric regression