Jing He, Wei Xiong, Maozai Tian

【Abstract】

High dimensional data analysis is of more concerned in nowadays research. Nonparametric approaches, due to its flexibility and no assumption of model specification, enjoy great popularity and recognition. Additive models, among them, can not only effectively reduce variable dimensions to avoid “the curse of dimensionality”, but also present marginal effects of each variable, thus have better interpretations of the response can be completely depicted by taking different quantile levels, moreover, no restrictions of the error distribution make quantile regression approach more robust and wider applicable. Combine those above advantages, local linear minimizing the check function method and local linear double kernel method are proposed in this paper to provide the non-crossing quantile curves. Furthermore, Monte Carlo simulation studies show that the proposed methods are superior to classical mean regression methods. Finally, a real data, Beijing second-hand housing price, is applied to illustrate our proposed methods.

【Keywords】

additive models, quantile regression, local linear minimizing the check function method, local linear double kernel method, marginal integration method