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

Authors :
Fanrong Zhao
Baoxue Zhang
Source :
Mathematics, Vol 12, Iss 16, p 2588 (2024)
Publication Year :
2024
Publisher :
MDPI AG, 2024.

Abstract

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.

Details

Language :
English
ISSN :
22277390
Volume :
12
Issue :
16
Database :
Directory of Open Access Journals
Journal :
Mathematics
Publication Type :
Academic Journal
Accession number :
edsdoj.55f5bd2ba2dd40fdb5bcccba57e06c51
Document Type :
article
Full Text :
https://doi.org/10.3390/math12162588