Optimal Nonparametric Inference with Two-Scale Distributional Nearest Neighbors

Understand

The weighted nearest neighbors (WNN) estimator has been popularly used as a flexible and easy-to-implement nonparametric tool for mean regression estimation.

• The bagging technique is an elegant way to form WNN estimators with weights automatically generated to the nearest neighbors; we name the resulting estimator as the distributional nearest neighbors (DNN) for easy reference.
• Yet, there is a lack of distributional results for such estimator, limiting its application to statistical inference.
• Moreover, when the mean regression function has higher-order smoothness, DNN does not achieve the optimal nonparametric convergence rate, mainly because of the bias issue.