Determining confidence interval and asymptotic distribution for parameters of multiresponse semiparametric regression model using smoothing spline estimator
The multiresponse semiparametric regression (MSR) model is a regression model with more than two response variables that are mutually correlated, and its regression function is composed of parametric and nonparametric components. The study objectives are propose a new method for estimating the MSR m...
| Главные авторы: | , , , |
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| Формат: | Статья |
| Язык: | English |
| Опубликовано: |
Elsevier
2023-07-01
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| Серии: | Journal of King Saud University: Science |
| Предметы: | |
| Online-ссылка: | http://www.sciencedirect.com/science/article/pii/S101836472300126X |
| _version_ | 1827926656284622848 |
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| author | Budi Lestari Nur Chamidah I. Nyoman Budiantara Dursun Aydin |
| author_facet | Budi Lestari Nur Chamidah I. Nyoman Budiantara Dursun Aydin |
| author_sort | Budi Lestari |
| collection | DOAJ |
| description | The multiresponse semiparametric regression (MSR) model is a regression model with more than two response variables that are mutually correlated, and its regression function is composed of parametric and nonparametric components. The study objectives are propose a new method for estimating the MSR model using smoothing spline. Also, find the confidence interval (CI) of parameters and the distribution asymptotically of the model parameters estimator. Methods used in this study are reproducing kernel Hilbert space (RKHS) method and a developed penalized weighted least squares (PWLS), and apply pivotal quantity, central limit theorem, and theorems of Cramer-Wold and Slutsky. The results are an 100(1–α)% CI estimate and an asymptotic normal distribution for the parameters of the MSR model. In conclusion, the estimated MSR model is a combined components estimate of parametric and nonparametric which is linear to observation, and CIs of parameters depend on t distribution and estimator of parameters is asymptotically normally distributed. Future time, this study results can be used as theoretical bases to design standard growth charts of the toddlers which can then be used to assess the nutritional status of the toddlers. |
| first_indexed | 2024-03-13T05:39:54Z |
| format | Article |
| id | doaj.art-c2b4cf5f1c0843a19b05f9d372a12b9d |
| institution | Directory Open Access Journal |
| issn | 1018-3647 |
| language | English |
| last_indexed | 2024-03-13T05:39:54Z |
| publishDate | 2023-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of King Saud University: Science |
| spelling | doaj.art-c2b4cf5f1c0843a19b05f9d372a12b9d2023-06-14T04:32:47ZengElsevierJournal of King Saud University: Science1018-36472023-07-01355102664Determining confidence interval and asymptotic distribution for parameters of multiresponse semiparametric regression model using smoothing spline estimatorBudi Lestari0Nur Chamidah1I. Nyoman Budiantara2Dursun Aydin3Department of Mathematics, Faculty of Mathematics and Natural Sciences, The University of Jember, Jember 68121 IndonesiaDepartment of Mathematics, Faculty of Science and Technology, Airlangga University, Surabaya 60115 Indonesia; Corresponding author.Department of Statistics, Faculty of Sciences and Data Analytics, Sepuluh Nopember Institute of Technology, Surabaya 60111 IndonesiaDepartment of Statistics, Faculty of Science, Muğla Sıtkı Koçman University, Muğla 48000 TurkeyThe multiresponse semiparametric regression (MSR) model is a regression model with more than two response variables that are mutually correlated, and its regression function is composed of parametric and nonparametric components. The study objectives are propose a new method for estimating the MSR model using smoothing spline. Also, find the confidence interval (CI) of parameters and the distribution asymptotically of the model parameters estimator. Methods used in this study are reproducing kernel Hilbert space (RKHS) method and a developed penalized weighted least squares (PWLS), and apply pivotal quantity, central limit theorem, and theorems of Cramer-Wold and Slutsky. The results are an 100(1–α)% CI estimate and an asymptotic normal distribution for the parameters of the MSR model. In conclusion, the estimated MSR model is a combined components estimate of parametric and nonparametric which is linear to observation, and CIs of parameters depend on t distribution and estimator of parameters is asymptotically normally distributed. Future time, this study results can be used as theoretical bases to design standard growth charts of the toddlers which can then be used to assess the nutritional status of the toddlers.http://www.sciencedirect.com/science/article/pii/S101836472300126XAsymptotic distributionConfidence intervalNutritional statusSemiparametric regressionSmoothing spline |
| spellingShingle | Budi Lestari Nur Chamidah I. Nyoman Budiantara Dursun Aydin Determining confidence interval and asymptotic distribution for parameters of multiresponse semiparametric regression model using smoothing spline estimator Journal of King Saud University: Science Asymptotic distribution Confidence interval Nutritional status Semiparametric regression Smoothing spline |
| title | Determining confidence interval and asymptotic distribution for parameters of multiresponse semiparametric regression model using smoothing spline estimator |
| title_full | Determining confidence interval and asymptotic distribution for parameters of multiresponse semiparametric regression model using smoothing spline estimator |
| title_fullStr | Determining confidence interval and asymptotic distribution for parameters of multiresponse semiparametric regression model using smoothing spline estimator |
| title_full_unstemmed | Determining confidence interval and asymptotic distribution for parameters of multiresponse semiparametric regression model using smoothing spline estimator |
| title_short | Determining confidence interval and asymptotic distribution for parameters of multiresponse semiparametric regression model using smoothing spline estimator |
| title_sort | determining confidence interval and asymptotic distribution for parameters of multiresponse semiparametric regression model using smoothing spline estimator |
| topic | Asymptotic distribution Confidence interval Nutritional status Semiparametric regression Smoothing spline |
| url | http://www.sciencedirect.com/science/article/pii/S101836472300126X |
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