广义函数型部分变系数混合模型的估计  

Estimation for Generalized Functional Partially Varying Coefficient Hybrid Models

作　　者：刘艳霞 王芝皓 芮荣祥 田茂再[1,2,3] LIU Yanxia;WANG Zhihao;RUI Rongxiang;TIAN Maozai(Center for Applied Statistics,School of Statistics,Renmin University of China,Beijing 100872;School of Statistics and Data Science,Xinjiang University of Finance and Economics,Urumqi 830012;School of Statistics,Lanzhou University of Finance and Economics,Lanzhou 730020)

机构地区：[1]中国人民大学应用统计科学研究中心,中国人民大学统计学院,北京100872 [2]新疆财经大学统计与数据科学学院,乌鲁木齐830012 [3]兰州财经大学统计学院,兰州730020

出　　处：《系统科学与数学》2021年第6期1742-1760,共19页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11861042);全国统计科学研究项目重点项目(2020LZ25)资助课题。

摘　　要：将广义变系数回归模型与广义函数型线性回归模型相结合,提出了一种新的模型——广义函数型部分变系数混合模型.基于函数型主成分基和B-样条基的方法,通过最大化拟似然函数得到了未知函数的估计,并在一定的正则条件下得到了各估计量的收敛速度及预测精度.通过数值模拟展现了模型的可行性和优越性,最后将所建模型应用到Tecator数据说明了模型的实用性.In this paper,a novel generalized functional partially varying coefficient hybrid models is proposed,which combines the generalized varying coefficient regression model with the generalized functional linear regression model.Based on the method of functional principal component base and B-splines base,the estimation of unknown functions is obtained by maximizing quasi-likelihood function,and the convergence rate and prediction accuracy of each estimator are obtained under certain regular conditions.The feasibility and superiority of the model are demonstrated by numerical simulation,and the practicability of the model is illustrated by applying the model to Tecator data.

关 键 词：函数型数据分析 广义变系数 部分函数型回归 收敛速度 混合数据 

分 类 号：O212.1[理学—概率论与数理统计]