Semiparametric Model Averaging for Ultrahigh-Dimensional Conditional Quantile Prediction  

作　　者：Chao Hui GUO Jing LV Hu YANG Jing Wen TU Chen Xiao TIAN 

机构地区：[1]School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China [2]School of Mathematics and Statistics,Southwest University,Chongqing 400715,P.R.China [3]College of Mathematics and Statistics,Chongqing University,Chongqing 401331,P.R.China [4]College of Finance,University of International Business and Economics,Beijing 100020,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第6期1171-1202,共32页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China Grant(Grant No.12201091);Natural Science Foundation of Chongqing Grant(Grant Nos.CSTB2022NSCQ-MSX0852,cstc2021jcyj-msxmX0502);Innovation Support Program for Chongqing Overseas Returnees(Grant No.cx2020025);Science and Technology Research Program of Chongqing Municipal Education Commission(Grant Nos.KJQN202100526,KJQN201900511);the National Statistical Science Research Program(Grant No.2022LY019);Chongqing University Innovation Research Group Project:Nonlinear Optimization Method and Its Application(Grant No.CXQT20014)。

摘　　要：In this paper,we develop a flexible semiparametric model averaging marginal regression procedure to forecast the joint conditional quantile function of the response variable for ultrahighdimensional data.First,we approximate the joint conditional quantile function by a weighted average of one-dimensional marginal conditional quantile functions that have varying coefficient structures.Then,a local linear regression technique is employed to derive the consistent estimates of marginal conditional quantile functions.Second,based on estimated marginal conditional quantile functions,we estimate and select the significant model weights involved in the approximation by a nonconvex penalized quantile regression.Under some relaxed conditions,we establish the asymptotic properties for the nonparametric kernel estimators and oracle estimators of the model averaging weights.We further derive the oracle property for the proposed nonconvex penalized model averaging procedure.Finally,simulation studies and a real data analysis are conducted to illustrate the merits of our proposed model averaging method.

关 键 词：Kernel regression model averaging oracle property penalized quantile regression ultrahigh-dimension data 

分 类 号：O212.1[理学—概率论与数理统计]