Novel efficient estimators of finite population mean in stratified random sampling with application

Khazan Sher; Muhammad Ameeq; Muhammad Muneeb Hassan; Basem A. Alkhaleel; Sidra Naz; Olyan Albalawi; Khazan Sher; Muhammad Ameeq; Muhammad Muneeb Hassan; Basem A. Alkhaleel; Sidra Naz; Olyan Albalawi

doi:10.3934/math.2025254

AIMS Mathematics

2025, Volume 10, Issue 3: 5495-5531. doi: 10.3934/math.2025254

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Research article

Novel efficient estimators of finite population mean in stratified random sampling with application

1.
Department of Statistics University of Peshawar, Pakistan
2.
Department of Statistics, The Islamia University Bahawalpur, Punjab Pakistan
3.
Department of Industrial Engineering, King Saud University, Riyadh 12372, Saudi Arabia
4.
Department of Statistics, Faculty of Science, University of Tabuk Saudi Arabia

Received: 09 December 2024 Revised: 07 February 2025 Accepted: 04 March 2025 Published: 11 March 2025
MSC : 62D

Unbiased estimators are valuable when no auxiliary information is available beyond the primary study variables. However, once auxiliary information is accessible, biased estimators with smaller Mean Square Error (MSE) often outperform unbiased estimators that have large variances. We sought to develop new estimators that incorporate a single auxiliary variable in stratified random sampling. This study contributes to the field by introducing two distinct families of estimators designed to estimate the finite population mean. We conducted a theoretical evaluation of the estimators' performance by examining bias and MSE derived under first-order approximation. Additionally, we established the theoretical conditions necessary for the proposed estimator families to exhibit superior performance compared with existing alternatives. Empirical and simulation-based studies demonstrated significant improvements in estimators over competing estimators for finite-population parameter estimation.
- unbiasedness,
- auxiliary,
- stratified random sampling,
- efficiency,
- mean square error
Citation: Khazan Sher, Muhammad Ameeq, Muhammad Muneeb Hassan, Basem A. Alkhaleel, Sidra Naz, Olyan Albalawi. Novel efficient estimators of finite population mean in stratified random sampling with application[J]. AIMS Mathematics, 2025, 10(3): 5495-5531. doi: 10.3934/math.2025254

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Abstract

Unbiased estimators are valuable when no auxiliary information is available beyond the primary study variables. However, once auxiliary information is accessible, biased estimators with smaller Mean Square Error (MSE) often outperform unbiased estimators that have large variances. We sought to develop new estimators that incorporate a single auxiliary variable in stratified random sampling. This study contributes to the field by introducing two distinct families of estimators designed to estimate the finite population mean. We conducted a theoretical evaluation of the estimators' performance by examining bias and MSE derived under first-order approximation. Additionally, we established the theoretical conditions necessary for the proposed estimator families to exhibit superior performance compared with existing alternatives. Empirical and simulation-based studies demonstrated significant improvements in estimators over competing estimators for finite-population parameter estimation.

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