Abstract
New nearest neighbor estimators of the nonparametric regression function and its derivatives are developed. Asymptotic normality is obtained for the proposed estimators over the interior points and the boundary region. Connections with other estimators such as local polynomial smoothers are established. The proposed estimators are boundary adaptive and extensions of the Stute estimators. Asymptotic minimax risk properties are also established for the proposed estimators. Simulations are conducted to compare the performance of the proposed estimators with others.
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