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

Fanrong Zhao and Baoxue Zhang ()
Additional contact information
Fanrong Zhao: School of Mathematics and Statistics, Shanxi University, Taiyuan 030006, China
Baoxue Zhang: School of Statistics, Capital University of Economics and Business, Beijing 100070, China

Mathematics, 2024, vol. 12, issue 16, 1-23

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.

Keywords: asymptotic normality; functional partially linear regression model; Nadaraya–Watson estimate; U-statistic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/16/2588/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/16/2588/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:16:p:2588-:d:1461124

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().