Robust Estimation for Partial Functional Linear Regression Model Based on Modal Regression  

作　　者：YU Ping ZHU Zhongyi SHI Jianhong AI Xikai 

机构地区：[1]School of Mathematics and Computer Science,Shanxi Normal University,Linfen 041000,China [2]Department of Statistics,Fudan University,Shanghai 200433,China

出　　处：《Journal of Systems Science & Complexity》2020年第2期527-544,共18页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.11671096,11690013,11731011。

摘　　要：This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression,which combines the common linear model with the functional linear regression model.The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error cases.The slope function is fitted by B-spline.Under suitable conditions,the authors obtain the convergence rates and asymptotic normality of the estimators.Finally,simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method.Both the simulation results and the real data analysis confirm that the newly proposed method works very well.

关 键 词：B-SPLINE functional data analysis functional linear model modal regression 

分 类 号：O212.1[理学—概率论与数理统计]