A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model

Autor:	Fanrong Zhao, Baoxue Zhang
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	asymptotic normality functional partially linear regression model Nadaraya–Watson estimate U-statistic Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 16, p 2588 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12162588
Popis:	The functional partially linear regression model comprises a functional linear part and a non-parametric part. Testing the linear relationship between the response and the functional predictor is of fundamental importance. In cases where functional data cannot be approximated with a few principal components, we develop a second-order U-statistic using a pseudo-estimate for the unknown non-parametric component. Under some regularity conditions, the asymptotic normality of the proposed test statistic is established using the martingale central limit theorem. The proposed test is evaluated for finite sample properties through simulation studies and its application to real data.
Databáze:	Directory of Open Access Journals
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