Auxiliary-Driven Transformations for Efficient Mean Estimation Under Stratified Systematic Sampling
- 1Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia
- 2Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O.Box 84428, Riyadh 11671, Saudi Arabia
Abstract
This study proposes a flexible family of mean estimators for finite populations under stratified systematic sampling by combining power transformations with an exponential adjustment. The proposed family allows different estimator forms through suitable choices of transformation parameters and stratum-specific characteristics of the auxiliary variable. In particular, the exponential component is constructed using transformations based on the within-stratum standard deviation, mid-range, range, relative range, coefficient of variation, skewness, and excess kurtosis, together with selected combinations of these measures. The bias and mean squared error (MSE) of the proposed estimators are derived using a first-order Taylor approximation, and optimal values of the unknown constants are obtained by minimizing the MSE. Theoretical efficiency conditions are also established against several existing estimators. To assess the practical performance of the proposed family, extensive Monte Carlo simulations are conducted under different finite-population structures, followed by empirical evaluation using three real populations. The performance of the competing estimators is compared in terms of bias, MSE, root mean squared error (RMSE), and percent relative efficiency (PRE). A sensitivity analysis is also performed to examine the effects of the transformation and exponential adjustment parameters. The numerical results demonstrate the potential of the proposed family to achieve improved estimation efficiency across different population structures and provide a flexible framework for utilizing auxiliary information under stratified systematic sampling.
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BibTeX
@article{alrweili2026auxiliarydriven,
title = {{Auxiliary-Driven Transformations for Efficient Mean Estimation Under Stratified Systematic Sampling}},
author = {Hleil Alrweili and Fatimah A. Almulhim},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14213875},
url = {https://www.mdpi.com/2227-7390/14/21/3875},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Auxiliary-Driven Transformations for Efficient Mean Estimation Under Stratified Systematic Sampling
AU - Hleil Alrweili
AU - Fatimah A. Almulhim
PY - 2026
DA - 2026/10/23
JO - Mathematics
DO - 10.3390/math14213875
UR - https://www.mdpi.com/2227-7390/14/21/3875
AB - This study proposes a flexible family of mean estimators for finite populations under stratified systematic sampling by combining power transformations with an exponential adjustment. The proposed family allows different estimator forms through suitable choices of transformation parameters and stratum-specific characteristics of the auxiliary variable. In particular, the exponential component is constructed using transformations based on the within-stratum standard deviation, mid-range, range, relative range, coefficient of variation, skewness, and excess kurtosis, together with selected combinations of these measures. The bias and mean squared error (MSE) of the proposed estimators are derived using a first-order Taylor approximation, and optimal values of the unknown constants are obtained by minimizing the MSE. Theoretical efficiency conditions are also established against several existing estimators. To assess the practical performance of the proposed family, extensive Monte Carlo simulations are conducted under different finite-population structures, followed by empirical evaluation using three real populations. The performance of the competing estimators is compared in terms of bias, MSE, root mean squared error (RMSE), and percent relative efficiency (PRE). A sensitivity analysis is also performed to examine the effects of the transformation and exponential adjustment parameters. The numerical results demonstrate the potential of the proposed family to achieve improved estimation efficiency across different population structures and provide a flexible framework for utilizing auxiliary information under stratified systematic sampling.
SN - 2227-7390
ER -