A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model
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 co...
| Published in: | Mathematics |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-08-01
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| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/16/2588 |
| Summary: | 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. |
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| ISSN: | 2227-7390 |