Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components Model
The objective of this work is to propose the iteratively reweighted least squares concept to form a fiducial generalized pivotal quantity of the between-group variance component for the unbalanced variance components model. The fiducial generalized pivotal quantity is a subclass of the generalized p...
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| author | Arisa Jiratampradab Jiraphan Suntornchost Thidaporn Supapakorn |
| author_facet | Arisa Jiratampradab Jiraphan Suntornchost Thidaporn Supapakorn |
| author_sort | Arisa Jiratampradab |
| collection | DOAJ |
| description | The objective of this work is to propose the iteratively reweighted least squares concept to form a fiducial generalized pivotal quantity of the between-group variance component for the unbalanced variance components model. The fiducial generalized pivotal quantity is a subclass of the generalized pivotal quantity which is useful technique to deal with problem of nuisance parameters for finding interval estimator. This research provides the probability distribution and the properties of the statistics to lead the constructing of the confidence interval. The authors also prove the construction of the fiducial generalized pivotal quantity through iteratively reweighted least squares. The performance comparison for the new proposed method with other competing methods in the literature is studied through a simulation study. The results of the simulation study demonstrate that the proposed method is very satisfactory in terms of both the coverage probability and the average width of the confidence interval. Furthermore, the analysis of real data for patients of sickle cell disease also illustrates that the proposed method gives the smallest average width of the confidence interval. All these results confirm that the iteratively reweighted least squares fiducial generalized pivotal quantity confidence interval is recommended. |
| format | Article |
| id | doaj-art-de7006d8564840b5b731e729f0e9f40c |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-de7006d8564840b5b731e729f0e9f40c2025-01-10T13:18:25ZengMDPI AGMathematics2227-73902025-01-0113115310.3390/math13010153Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components ModelArisa Jiratampradab0Jiraphan Suntornchost1Thidaporn Supapakorn2Department of Statistics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, ThailandDepartment of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, ThailandDepartment of Statistics, Faculty of Science, Kasetsart University, Bangkok 10900, ThailandThe objective of this work is to propose the iteratively reweighted least squares concept to form a fiducial generalized pivotal quantity of the between-group variance component for the unbalanced variance components model. The fiducial generalized pivotal quantity is a subclass of the generalized pivotal quantity which is useful technique to deal with problem of nuisance parameters for finding interval estimator. This research provides the probability distribution and the properties of the statistics to lead the constructing of the confidence interval. The authors also prove the construction of the fiducial generalized pivotal quantity through iteratively reweighted least squares. The performance comparison for the new proposed method with other competing methods in the literature is studied through a simulation study. The results of the simulation study demonstrate that the proposed method is very satisfactory in terms of both the coverage probability and the average width of the confidence interval. Furthermore, the analysis of real data for patients of sickle cell disease also illustrates that the proposed method gives the smallest average width of the confidence interval. All these results confirm that the iteratively reweighted least squares fiducial generalized pivotal quantity confidence interval is recommended.https://www.mdpi.com/2227-7390/13/1/153iteratively reweighted least squaresbetween-group variance componentcoverage probabilityvariance components modelfiducial generalized pivotal quantity |
| spellingShingle | Arisa Jiratampradab Jiraphan Suntornchost Thidaporn Supapakorn Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components Model Mathematics iteratively reweighted least squares between-group variance component coverage probability variance components model fiducial generalized pivotal quantity |
| title | Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components Model |
| title_full | Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components Model |
| title_fullStr | Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components Model |
| title_full_unstemmed | Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components Model |
| title_short | Iteratively Reweighted Least Squares Fiducial Interval for Variance in Unbalanced Variance Components Model |
| title_sort | iteratively reweighted least squares fiducial interval for variance in unbalanced variance components model |
| topic | iteratively reweighted least squares between-group variance component coverage probability variance components model fiducial generalized pivotal quantity |
| url | https://www.mdpi.com/2227-7390/13/1/153 |
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