Central limit theorems for the integrated squared error of derivative estimators

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Date

2007-02-21T14:39:44Z

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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.

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Keywords

Central limit theorem, Integrated squared error, Kernel estimates, Local polynomial estimate, Nadaraya-Watson estimate, Nonparametric regression

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