Partially Functional Linear Models with Linear Process Errors
In this paper, we focus on the partial functional linear model with linear process errors deduced by not necessarily independent random variables. Based on Mercer’s theorem and Karhunen–Loève expansion, we give the estimators of the slope parameter and coefficient function in the model, establish th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/16/3581 |
| _version_ | 1797583955762872320 |
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| author | Yanping Hu Zhongqi Pang |
| author_facet | Yanping Hu Zhongqi Pang |
| author_sort | Yanping Hu |
| collection | DOAJ |
| description | In this paper, we focus on the partial functional linear model with linear process errors deduced by not necessarily independent random variables. Based on Mercer’s theorem and Karhunen–Loève expansion, we give the estimators of the slope parameter and coefficient function in the model, establish the asymptotic normality of the estimator for the parameter and discuss the weak convergence with rates of the proposed estimators. Meanwhile, the penalized estimator of the parameter is defined by the SCAD penalty and its oracle property is investigated. Finite sample behavior of the proposed estimators is also analysed via simulations. |
| first_indexed | 2024-03-10T23:45:30Z |
| format | Article |
| id | doaj.art-4ec2c04140ca4f36b897e41dca838da3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:45:30Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4ec2c04140ca4f36b897e41dca838da32023-11-19T02:04:04ZengMDPI AGMathematics2227-73902023-08-011116358110.3390/math11163581Partially Functional Linear Models with Linear Process ErrorsYanping Hu0Zhongqi Pang1School of Mathematical Sciences, Tongji University, Shanghai 200092, ChinaDepartment of Applied Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou 215123, ChinaIn this paper, we focus on the partial functional linear model with linear process errors deduced by not necessarily independent random variables. Based on Mercer’s theorem and Karhunen–Loève expansion, we give the estimators of the slope parameter and coefficient function in the model, establish the asymptotic normality of the estimator for the parameter and discuss the weak convergence with rates of the proposed estimators. Meanwhile, the penalized estimator of the parameter is defined by the SCAD penalty and its oracle property is investigated. Finite sample behavior of the proposed estimators is also analysed via simulations.https://www.mdpi.com/2227-7390/11/16/3581symptotic normalityconvergence ratelinear process errorpartial functional linear modelvariable selection |
| spellingShingle | Yanping Hu Zhongqi Pang Partially Functional Linear Models with Linear Process Errors Mathematics symptotic normality convergence rate linear process error partial functional linear model variable selection |
| title | Partially Functional Linear Models with Linear Process Errors |
| title_full | Partially Functional Linear Models with Linear Process Errors |
| title_fullStr | Partially Functional Linear Models with Linear Process Errors |
| title_full_unstemmed | Partially Functional Linear Models with Linear Process Errors |
| title_short | Partially Functional Linear Models with Linear Process Errors |
| title_sort | partially functional linear models with linear process errors |
| topic | symptotic normality convergence rate linear process error partial functional linear model variable selection |
| url | https://www.mdpi.com/2227-7390/11/16/3581 |
| work_keys_str_mv | AT yanpinghu partiallyfunctionallinearmodelswithlinearprocesserrors AT zhongqipang partiallyfunctionallinearmodelswithlinearprocesserrors |