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...
| 發表在: | Mathematics |
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| Main Authors: | , |
| 格式: | Article |
| 語言: | 英语 |
| 出版: |
MDPI AG
2024-08-01
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| 主題: | |
| 在線閱讀: | https://www.mdpi.com/2227-7390/12/16/2588 |
| _version_ | 1849856308632616960 |
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| author | Fanrong Zhao Baoxue Zhang |
| author_facet | Fanrong Zhao Baoxue Zhang |
| author_sort | Fanrong Zhao |
| collection | DOAJ |
| container_title | Mathematics |
| description | 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. |
| format | Article |
| id | doaj-art-55f5bd2ba2dd40fdb5bcccba57e06c51 |
| institution | Directory of Open Access Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| spelling | doaj-art-55f5bd2ba2dd40fdb5bcccba57e06c512025-08-20T01:21:43ZengMDPI AGMathematics2227-73902024-08-011216258810.3390/math12162588A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression ModelFanrong Zhao0Baoxue Zhang1School of Mathematics and Statistics, Shanxi University, Taiyuan 030006, ChinaSchool of Statistics, Capital University of Economics and Business, Beijing 100070, ChinaThe 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.https://www.mdpi.com/2227-7390/12/16/2588asymptotic normalityfunctional partially linear regression modelNadaraya–Watson estimateU-statistic |
| spellingShingle | Fanrong Zhao Baoxue Zhang A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model asymptotic normality functional partially linear regression model Nadaraya–Watson estimate U-statistic |
| title | A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model |
| title_full | A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model |
| title_fullStr | A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model |
| title_full_unstemmed | A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model |
| title_short | A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model |
| title_sort | u statistic for testing the lack of dependence in functional partially linear regression model |
| topic | asymptotic normality functional partially linear regression model Nadaraya–Watson estimate U-statistic |
| url | https://www.mdpi.com/2227-7390/12/16/2588 |
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