Minimax Rate Optimal Adaptive Nearest Neighbor Classification and Regression

k Nearest Neighbor (kNN) method is a simple and popular statistical for classification regression. For both regression problems, existing works have shown that, if the distribution of feature vector has bounded support probability density function away from zero in its support, convergence rate standard kNN method, which same all test samples, minimax optimal. On contrary, unbounded we show that there gap between achieved by bound. To close this gap, propose an adaptive different selected samples. Our selection rule does not require precise knowledge underlying features. The proposed significantly outperforms one. We characterize it matches lower