Central limit theorems for the integrated squared error of derivative estimators
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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.
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Central limit theorem, Integrated squared error, Kernel estimates, Local polynomial estimate, Nadaraya-Watson estimate, Nonparametric regression