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...

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Main Authors: Abdulaziz S. Alghamdi, Fatimah A. Almulhim
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/10/1635
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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).
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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