变系数部分函数型线性模型的复合分位数回归估计  

Composite Quantile Regression Estimation for Varying Coefficient Partially Functional Linear Models

作　　者：刘艳霞 王芝皓 田茂再[2,3,4] LIU Yan-xia;WANG Zhi-hao;TIAN Mao-zai(College of Science,North China Institute of Science and Technology,Langfang 065201,China;School of Statistics,Renmin University of China,Beijing 100872,China;School of Statistics and Information,Xinjiang University of Finance and Economics,Urumqi 830012,China;School of Statistics,Lanzhou University of Finance and Economics,Lanzhou 730020,China)

机构地区：[1]华北科技学院理学院,河北廊坊065201 [2]中国人民大学统计学院,北京100872 [3]新疆财经大学统计与信息学院,新疆乌鲁木齐830012 [4]兰州财经大学统计学院,甘肃兰州730020

出　　处：《数理统计与管理》2025年第2期227-238,共12页Journal of Applied Statistics and Management

基　　金：中国人民大学科学研究基金(中央高校基本科研业务费专项资金资助)(18XNL012);中央高校基本科研业务费资助(3142023039);华北科技学院应用统计重点学科;廊坊市科技支撑项目(2024011081)。

摘　　要：针对变系数部分函数型线性模型的函数系数估计问题,提出了一种新的估计方法,即基于函数型主成分基和B样条基,通过最小化复合分位数损失函数得到了未知函数系数的估计。并在若干正则条件下,得到了各估计量的收敛速度。通过数值模拟展现了所提估计方法的可行性和优越性,最后将所提估计方法应用到Tecator数据说明了方法的实用性。A new estimation method is proposed for the function coefficient estimation problem of varying coefficient partially functional linear models.Based on the functional principal component basis and B spline basis,the unknown function coefficients are estimated by minimizing the loss of composite quantile.Under some regular conditions,the convergence rate of each estimator is obtained.Numerical simulation shows the feasibility and superiority of the proposed estimation method.Finally,the application of the proposed estimation method to Tecator data illustrates the practicability of the method.

关 键 词：变系数 B样条 复合分位数回归 函数型数据 函数型主成分分析 

分 类 号：O212[理学—概率论与数理统计]