A0498
Title: Optimal nonparametric inference with two-scale distributional nearest neighbors
Authors: Yingying Fan - University of Southern California (United States)
Jinchi Lv - University of Southern California (United States)
Emre Demirkaya - University of Tennesse, Knoxville (United States)
Patrick Vossler - Standford University (United States)
Jingbo Wang - University of Southern California (United States)
Lan Gao - University of Tennessee Knoxville (United States) [presenting]
Abstract: The weighted nearest neighbours (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 neighbours; the resulting estimator as the distributional nearest neighbours (DNN) for easy reference is named. Yet, there is a lack of distributional results for such an 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. An in-depth technical analysis of the DNN is provided, based on which a bias reduction approach for the DNN estimator is suggested by linearly combining two DNN estimators with different subsampling scales, resulting in the novel two-scale DNN (TDNN) estimator. The two-scale DNN estimator is proven to enjoy the optimal nonparametric convergence rate in estimating the regression function under the fourth-order smoothness condition. Further beyond estimation, it was established that the DNN and two-scale DNN are asymptotically normal as the subsampling scales and sample size diverge to infinity. The theoretical results and appealing finite-sample performance of the suggested two-scale DNN method are illustrated with simulation examples and a real data application.
