函数型线性回归模型的变点检验  

Detecting Changes in the Functional Linear Regression Model

作　　者：刘宣 马海强 LIU Xuan;MA Haiqiang(School of Mathematics and Information Science,Nanchang Normal University,Nanchang,330032,China;School of Statistics,Jiangxi University of Finance and Economics,Nanchang,330013,China)

机构地区：[1]南昌师范学院数学与信息科学学院,南昌330032 [2]江西财经大学统计学院,南昌330013

出　　处：《应用概率统计》2023年第4期475-490,共16页Chinese Journal of Applied Probability and Statistics

基　　金：江西省教育厅科技类重点项目(批准号:GJJ202603);南昌师范学院博士科研基金项目(批准号:NSBSJJ2020006);江西省教育厅一般项目(批准号:GJJ200522、GJJ200545)资助.

摘　　要：本文研究了解释变量为过程,响应变量为标量的函数型线性回归模型的变点检验问题.基于投影矩估计量,在截断的有限维空间上,论文给出了检验统计量和变点估计量,获得了检验统计量的渐近分布,并在一定的条件下证明了变点估计量的相合性.数值模拟和实际数据分析呈现了所提方法的有限样本表现.In this paper,we consider the change-point problems for the functional linear model,where the explanatory variable is a random process,and the response is a scalar.Based on the projecting moment estimators of the parameters onto the truncated nite-dimensional space,we propose the detecting statistic and give the estimator of the change-point.In a theoretical investigation,we derive the asymptotic distribution for the proposed detecting statistic,and establish the consistency of the change-point estimate under some mild conditions.Some simulation studies and a real data analysis are conducted to illustrate the nite performance of the proposed testing methods.

关 键 词：变点 函数型线性回归模型 投影 布朗桥 

分 类 号：O212.1[理学—概率论与数理统计]