Testing Linearity in Functional Partially Linear Models  

作　　者：Fan-rong ZHAO Bao-xue ZHANG 

机构地区：[1]School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China [2]School of Statistics,Capital University of Economics and Business,Beijing 100070,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第3期875-886,共12页应用数学学报（英文版）

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

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 literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,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 functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.

关 键 词：asymptotic theory functional partially linear model Nadaraya-Watson estimate test statistic 

分 类 号：O212.1[理学—概率论与数理统计]