Quantile Regression under Local Misspecification  

作　　者：Xiao-gang DUAN Qi-hua WANG 

机构地区：[1]School of Statistics,Beijing Normal University,Beijing 100875,Chin [2]Academy of Mathematics and System Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Acta Mathematicae Applicatae Sinica》2020年第4期790-802,共13页应用数学学报（英文版）

基　　金：This paper is supported by the National Natural Science Foundation of China(No.11771049).

摘　　要：The frequentist model averaging(FMA)and the focus information criterion(FIC)under a local framework have been extensively studied in the likelihood and regression setting since the seminal work of Hjort and Claes kens in 2003.One inconvenience,however,of the existing works is that they usually require the involved criterion function to be twice differentiable which thus prevents a direct application to the case of quantile regression(QR).This as well as some other intrinsic merits of QR motivate us to study the FIC and FMA in a locally misspecified linear QR model.Specifically,we derive in this paper the explicit asymptotic risk expression for a general submodel-based QR estimator of a focus parameter.Then based on this asymptotic result,we develop the FIC and FMA in the current setting.Our theoretical development depends crucially on the convexity of the objective function,which makes possible to establish the asymptotics based on the existing convex stochastic process theory.Simulation studies are presented to illustrate the finite sample performance of the proposed method.The low birth weight data set is analyzed.

关 键 词：frequentist model averaging focus information criterion local framework quantile regression 

分 类 号：O212.1[理学—概率论与数理统计]