Central limit theorems for the integrated squared error of derivative estimators - Melanie Birke (Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2006)
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.
Keywords: 519; central limit theorem; integrated squared error; kernel estimates; local polynomial estimate; Nadaraya-Watson estimate; nonparametric regression