Least Square Estimation for Multiple Functional Linear Model with Autoregressive Errors  

作　　者：Meng WANG Ming-liang SHU Jian-jun ZHOU Si-xin WU Min CHEN 

机构地区：[1]School of Management,University of Science and Technology of China,Hefei 230026,China [2]Academy of Mathematics and System Science,Chinese Academy of Sciences,Beijing 100190,China [3]Yunnan Key Laboratory of Statistical Modeling and Data Analysis,Yunnan University,Kunming 650091,China

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第1期84-98,共15页应用数学学报(英文版)

基　　金：supported by National Nature Science Foundation of China(No.11861074,No.11371354 and N0.11301464);Key Laboratory of Random Complex Structures and Data Science,Chinese Academy of Sciences,Beijing 100190,China(No.2008DP173182);Applied Basic Research Project of Yunnan Province(No.2019FB138).

摘　　要：As an extension of linear regression in functional data analysis, functional linear regression has been studied by many researchers and applied in various fields. However, in many cases, data is collected sequentially over time, for example the financial series, so it is necessary to consider the autocorrelated structure of errors in functional regression background. To this end, this paper considers a multiple functional linear model with autoregressive errors. Based on the functional principal component analysis, we apply the least square procedure to estimate the functional coefficients and autoregression coefficients. Under some regular conditions, we establish the asymptotic properties of the proposed estimators. A simulation study is conducted to investigate the finite sample performance of our estimators. A real example on China's weather data is applied to illustrate the validity of our model.

关 键 词：multiple functional linear model autoregressive errors principal component analysis CONSISTENCY 

分 类 号：O212.1[理学—概率论与数理统计]