Testing Linearity in Functional Partially Linear Models

作     者：Fan-rong ZHAO Bao-xue ZHANG Fan-rong ZHAO;Bao-xue ZHANG

作者机构：School of Mathematical SciencesShanxi UniversityTaiyuan 030006China School of StatisticsCapital University of Economics and BusinessBeijing 100070China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2024年第40卷第3期

页      面：875-886页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(No.12271370) 

主　　题：asymptotic theory functional partially linear model Nadaraya-Watson estimate test statistic 

摘      要：For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing *** to test the correlation between response and explanatory variables,however,still seems to be ***,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope ***,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity ***,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.