标题：Weighted local linear composite quantile estimation for the case of general error distributions
作者：Sun, J.;Gai, Y.;Lin, L.
作者机构：[Sun, J] Shandong University Qilu Securities Institute for Financial Studies, School of Mathematics, Shandong University, China;[ Gai, Y] School of Ec 更多
通讯作者地址：[Lin, L]Shandong Univ, Qilu Secur Inst Financial Studies, Jinan, Peoples R China.
来源：Journal of Statistical Planning and Inference
关键词：Asymmetric distribution;Asymptotic efficiency;Consistency;Local linear composite quantile regression;Nonparametric regression
摘要：It is known that for nonparametric regression, local linear composite quantile regression (local linear CQR) is a more competitive technique than classical local linear regression since it can significantly improve estimation efficiency under a class of non-normal and symmetric error distributions. However, this method only applies to symmetric errors because, without symmetric condition, the estimation bias is non-negligible and therefore the resulting estimator is inconsistent. In this paper, we propose a weighted local linear CQR method for general error conditions. This method applies to both symmetric and asymmetric random errors. Because of the use of weights, the estimation bias is eliminated asymptotically and the asymptotic normality is established. Furthermore, by minimizing asymptotic variance, the optimal weights are computed and consequently the optimal estimate (the most efficient estimate) is obtained. By comparing relative efficiency theoretically or numerically, we can ensure that the new estimation outperforms the local linear CQR estimation. Finite sample behaviors conducted by simulation studies further illustrate the theoretical findings.