Optimizing Finite Population Mean Estimation Using Simulation and Empirical Data
Two-phase sampling is an effective sampling approach that is useful in sample surveys when prior auxiliary information is not available. When two variables have an association, the ranks of the auxiliary variable are proportional to the study variable. Therefore, we can use these rankings to improve...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/10/1635 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849711535659679744 |
|---|---|
| author | Abdulaziz S. Alghamdi Fatimah A. Almulhim |
| author_facet | Abdulaziz S. Alghamdi Fatimah A. Almulhim |
| author_sort | Abdulaziz S. Alghamdi |
| collection | DOAJ |
| description | Two-phase sampling is an effective sampling approach that is useful in sample surveys when prior auxiliary information is not available. When two variables have an association, the ranks of the auxiliary variable are proportional to the study variable. Therefore, we can use these rankings to improve the accuracy of the estimators. In this article, we estimate the overall mean of the study variable based on extreme values and the ranks of the auxiliary variable. The properties of the proposed estimators with respect to biases and mean squared errors (MSEs) in two-phase sampling are obtained up to first order approximation. We verify the theoretical results and assess the performance of the proposed estimators using three datasets and a simulation study, which show that the proposed estimators outperform other existing estimators in terms of percent relative efficiency (PRE). |
| format | Article |
| id | doaj-art-0bafdc4e4ae34eb592c863efeadfa22c |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-0bafdc4e4ae34eb592c863efeadfa22c2025-08-20T03:14:36ZengMDPI AGMathematics2227-73902025-05-011310163510.3390/math13101635Optimizing Finite Population Mean Estimation Using Simulation and Empirical DataAbdulaziz S. Alghamdi0Fatimah A. Almulhim1Department of Mathematics, College of Science & Arts, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi ArabiaDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaTwo-phase sampling is an effective sampling approach that is useful in sample surveys when prior auxiliary information is not available. When two variables have an association, the ranks of the auxiliary variable are proportional to the study variable. Therefore, we can use these rankings to improve the accuracy of the estimators. In this article, we estimate the overall mean of the study variable based on extreme values and the ranks of the auxiliary variable. The properties of the proposed estimators with respect to biases and mean squared errors (MSEs) in two-phase sampling are obtained up to first order approximation. We verify the theoretical results and assess the performance of the proposed estimators using three datasets and a simulation study, which show that the proposed estimators outperform other existing estimators in terms of percent relative efficiency (PRE).https://www.mdpi.com/2227-7390/13/10/1635study variableauxiliary informationminimum/maximum valuesranksbiaspercent relative efficiency |
| spellingShingle | Abdulaziz S. Alghamdi Fatimah A. Almulhim Optimizing Finite Population Mean Estimation Using Simulation and Empirical Data Mathematics study variable auxiliary information minimum/maximum values ranks bias percent relative efficiency |
| title | Optimizing Finite Population Mean Estimation Using Simulation and Empirical Data |
| title_full | Optimizing Finite Population Mean Estimation Using Simulation and Empirical Data |
| title_fullStr | Optimizing Finite Population Mean Estimation Using Simulation and Empirical Data |
| title_full_unstemmed | Optimizing Finite Population Mean Estimation Using Simulation and Empirical Data |
| title_short | Optimizing Finite Population Mean Estimation Using Simulation and Empirical Data |
| title_sort | optimizing finite population mean estimation using simulation and empirical data |
| topic | study variable auxiliary information minimum/maximum values ranks bias percent relative efficiency |
| url | https://www.mdpi.com/2227-7390/13/10/1635 |
| work_keys_str_mv | AT abdulazizsalghamdi optimizingfinitepopulationmeanestimationusingsimulationandempiricaldata AT fatimahaalmulhim optimizingfinitepopulationmeanestimationusingsimulationandempiricaldata |