Estimation for spatial semi-functional partial linear regression model with missing response at random
The aim of this article is to study a semi-functional partial linear regression model (SFPLR) for spatial data with responses missing at random (MAR). The estimators are constructed using the kernel method, and some asymptotic properties, such as the probability convergence rates of the nonparametri...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-03-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2025-0108 |
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| author | Benchikh Tawfik Almanjahie Ibrahim M. Fetitah Omar Attouch Mohammed Kadi |
| author_facet | Benchikh Tawfik Almanjahie Ibrahim M. Fetitah Omar Attouch Mohammed Kadi |
| author_sort | Benchikh Tawfik |
| collection | DOAJ |
| description | The aim of this article is to study a semi-functional partial linear regression model (SFPLR) for spatial data with responses missing at random (MAR). The estimators are constructed using the kernel method, and some asymptotic properties, such as the probability convergence rates of the nonparametric component and the asymptotic distribution of the parametric and nonparametric components, are established under certain conditions. Next, the performance and superiority of these estimators are presented and examined through a study on simulated data, comparing our semi-functional partially linear model with the MAR estimator to the semi-functional partially linear model with the full-case estimator, and the functional nonparametric regression model estimator with MAR. The results indicate that the proposed estimators outperform traditional estimators as the amount of randomly missing data increases. Additionally, a study is conducted on real data regarding the modeling of pollution levels using our model, incorporating covariates such as average daily temperature as a functional variable, alongside maximum daily mixing height, total daily precipitation, and daily primary aerosol emission rates as explanatory variables. |
| format | Article |
| id | doaj-art-264941c539ee472181aa7231e045fdee |
| institution | DOAJ |
| issn | 2391-4661 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-264941c539ee472181aa7231e045fdee2025-08-20T03:01:57ZengDe GruyterDemonstratio Mathematica2391-46612025-03-0158111710.1515/dema-2025-0108Estimation for spatial semi-functional partial linear regression model with missing response at randomBenchikh Tawfik0Almanjahie Ibrahim M.1Fetitah Omar2Attouch Mohammed Kadi3Laboratory of Statistics and Stochastic Processes, University of Djillali Liabes BP 89, Sidi Bel Abbes 22000, AlgeriaDepartment of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi ArabiaLaboratory of Statistics and Stochastic Processes, University of Djillali Liabes BP 89, Sidi Bel Abbes 22000, AlgeriaLaboratory of Statistics and Stochastic Processes, University of Djillali Liabes BP 89, Sidi Bel Abbes 22000, AlgeriaThe aim of this article is to study a semi-functional partial linear regression model (SFPLR) for spatial data with responses missing at random (MAR). The estimators are constructed using the kernel method, and some asymptotic properties, such as the probability convergence rates of the nonparametric component and the asymptotic distribution of the parametric and nonparametric components, are established under certain conditions. Next, the performance and superiority of these estimators are presented and examined through a study on simulated data, comparing our semi-functional partially linear model with the MAR estimator to the semi-functional partially linear model with the full-case estimator, and the functional nonparametric regression model estimator with MAR. The results indicate that the proposed estimators outperform traditional estimators as the amount of randomly missing data increases. Additionally, a study is conducted on real data regarding the modeling of pollution levels using our model, incorporating covariates such as average daily temperature as a functional variable, alongside maximum daily mixing height, total daily precipitation, and daily primary aerosol emission rates as explanatory variables.https://doi.org/10.1515/dema-2025-0108missing at random datafunctional data analysisasymptotic normalityspatial datakernel regression method62h1262g0762g3562g20 |
| spellingShingle | Benchikh Tawfik Almanjahie Ibrahim M. Fetitah Omar Attouch Mohammed Kadi Estimation for spatial semi-functional partial linear regression model with missing response at random Demonstratio Mathematica missing at random data functional data analysis asymptotic normality spatial data kernel regression method 62h12 62g07 62g35 62g20 |
| title | Estimation for spatial semi-functional partial linear regression model with missing response at random |
| title_full | Estimation for spatial semi-functional partial linear regression model with missing response at random |
| title_fullStr | Estimation for spatial semi-functional partial linear regression model with missing response at random |
| title_full_unstemmed | Estimation for spatial semi-functional partial linear regression model with missing response at random |
| title_short | Estimation for spatial semi-functional partial linear regression model with missing response at random |
| title_sort | estimation for spatial semi functional partial linear regression model with missing response at random |
| topic | missing at random data functional data analysis asymptotic normality spatial data kernel regression method 62h12 62g07 62g35 62g20 |
| url | https://doi.org/10.1515/dema-2025-0108 |
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