Twofold Auxiliary Information Under Two-Phase Sampling: An Improved Family of Double-Transformed Variance Estimators
Outlier values and rankings are important for emphasizing data distribution variability, which improves the accuracy and effectiveness of variance estimations. To enhance the estimation of finite population variance in a two-phase sampling framework, this study presents an improved class of double e...
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MDPI AG
2025-01-01
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| author | Umer Daraz Della Agustiana Jinbiao Wu Walid Emam |
| author_facet | Umer Daraz Della Agustiana Jinbiao Wu Walid Emam |
| author_sort | Umer Daraz |
| collection | DOAJ |
| description | Outlier values and rankings are important for emphasizing data distribution variability, which improves the accuracy and effectiveness of variance estimations. To enhance the estimation of finite population variance in a two-phase sampling framework, this study presents an improved class of double exponential-type estimators by utilizing the outlier values and ranks of an auxiliary variable. A theoretical analysis is conducted to derive the biases and mean squared errors (MSEs) of these estimators using first-order approximations. A comprehensive simulation study is then performed to analyze the performance of the proposed estimators. The results clearly show that the new estimators provide more precise estimates, achieving a higher percentage relative efficiency (PRE) across all simulated scenarios. Furthermore, three data sets are analyzed to further confirm the efficiency of the proposed estimators as compared to other existing estimators. These results emphasize the potential of the proposed class of estimators to optimize variance estimation techniques, making it a more cost-effective and accurate choice for researchers using two-phase sampling in a variety of domains. |
| format | Article |
| id | doaj-art-fef330e59f3e455ab263cbb3ec366250 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-fef330e59f3e455ab263cbb3ec3662502025-01-24T13:22:18ZengMDPI AGAxioms2075-16802025-01-011416410.3390/axioms14010064Twofold Auxiliary Information Under Two-Phase Sampling: An Improved Family of Double-Transformed Variance EstimatorsUmer Daraz0Della Agustiana1Jinbiao Wu2Walid Emam3School of Mathematics and Statistics, Central South University, Changsha 410017, ChinaSchool of Metallurgy and Environment, Central South University, Changsha 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha 410017, ChinaDepartment of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaOutlier values and rankings are important for emphasizing data distribution variability, which improves the accuracy and effectiveness of variance estimations. To enhance the estimation of finite population variance in a two-phase sampling framework, this study presents an improved class of double exponential-type estimators by utilizing the outlier values and ranks of an auxiliary variable. A theoretical analysis is conducted to derive the biases and mean squared errors (MSEs) of these estimators using first-order approximations. A comprehensive simulation study is then performed to analyze the performance of the proposed estimators. The results clearly show that the new estimators provide more precise estimates, achieving a higher percentage relative efficiency (PRE) across all simulated scenarios. Furthermore, three data sets are analyzed to further confirm the efficiency of the proposed estimators as compared to other existing estimators. These results emphasize the potential of the proposed class of estimators to optimize variance estimation techniques, making it a more cost-effective and accurate choice for researchers using two-phase sampling in a variety of domains.https://www.mdpi.com/2075-1680/14/1/64double exponential estimatorsvariance estimationtwo-phase samplingoutlier valuesranksbias |
| spellingShingle | Umer Daraz Della Agustiana Jinbiao Wu Walid Emam Twofold Auxiliary Information Under Two-Phase Sampling: An Improved Family of Double-Transformed Variance Estimators Axioms double exponential estimators variance estimation two-phase sampling outlier values ranks bias |
| title | Twofold Auxiliary Information Under Two-Phase Sampling: An Improved Family of Double-Transformed Variance Estimators |
| title_full | Twofold Auxiliary Information Under Two-Phase Sampling: An Improved Family of Double-Transformed Variance Estimators |
| title_fullStr | Twofold Auxiliary Information Under Two-Phase Sampling: An Improved Family of Double-Transformed Variance Estimators |
| title_full_unstemmed | Twofold Auxiliary Information Under Two-Phase Sampling: An Improved Family of Double-Transformed Variance Estimators |
| title_short | Twofold Auxiliary Information Under Two-Phase Sampling: An Improved Family of Double-Transformed Variance Estimators |
| title_sort | twofold auxiliary information under two phase sampling an improved family of double transformed variance estimators |
| topic | double exponential estimators variance estimation two-phase sampling outlier values ranks bias |
| url | https://www.mdpi.com/2075-1680/14/1/64 |
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