M.: Smoothing regression quantile by combining k-NN estimation with local linear kernel fitting

Abstract: A two-step nonparametric regression quantile smoothing technique is presented here, combining a standard k-NN technique and a locally linear kernel smoother. There are many advantages to this approach: an asymptotically optimal mean square error (Fan, Hu and Truong (1995)), a ready-made bandwidth selection rule (Yu and Jones (1998)), and simple computation and flexible estimation under variable transformations and distributional assumptions. The method is tested on a simulated example, and applied to data. Key words and phrases: Bandwidth selection, correlated regression model, double kernel method, k-NN method, local linear kernel smoothing, mean square error, regression quantile. 1