An Improved Data Science Based Ratio-Type Estimator for Population Mean in Stratified Random Sampling Using Multi-Auxiliary Information

Abstract

This article proposed an improved data science ratio-type estimator for estimating the population mean of a study variable using multiple auxiliary variables in stratified sampling. In this paper, we present a comprehensive view on data science including various types of estimating advanced analytics and population methods that can be applied multiple auxiliary and capabilities. The theoretical properties of the proposed estimator are investigated, and its bias and mean square error (MSE) are derived under suitable assumptions. The efficiency of the proposed estimator is compared with that of the estimator proposed by Sharma and Kumar. The relative efficiency of the estimators is examined both theoretically and numerically. A numerical illustration is also presented to demonstrate the performance of the proposed estimator and to assess its efficiency in comparison with the existing estimator. The results indicate the effectiveness of the proposed estimator in improving the precision of population mean estimation in stratified sampling when multiple auxiliary variables.

Introduction

The text presents a new improved ratio-type estimator for estimating the population mean in stratified random sampling using multiple auxiliary variables.

• Purpose: Auxiliary variables can improve the precision of estimates when they are strongly correlated with the study variable. Ratio, product, regression, and difference estimators are commonly used for this purpose.
• Research gap: Previous studies developed ratio/product estimators using single or multiple auxiliary variables, but the authors aim to improve the Kadilar and Cingi estimator by incorporating multiple auxiliary variables.
• Sampling framework: The population is divided into homogeneous strata, and samples are selected from each stratum using simple random sampling without replacement. The study defines stratum means, population means, weights, variances, and covariances for the study variable Y and multiple auxiliary variables X1,…,Xk.
• Previous work: Studies by Bahl, Tuteja, Kumar, Sharma, Kadilar, Cingi, and others established ratio- and product-type estimators for single and multiple auxiliary variables in simple and stratified random sampling.
• Existing estimator: Sharma and Kumar proposed a multiple-auxiliary-variable exponential ratio estimator for stratified sampling. Its bias and mean squared error (MSE) were derived, along with optimum weights for the auxiliary variables.
• Proposed estimator: The authors modify the Kadilar and Cingi ratio estimator to use multiple auxiliary variables. The proposed estimator is

tstp=Qy?st∑i=1kλiX?ix?sti,

where Q is a modifying constant and λi are weights assigned to the auxiliary variables, satisfying

∑i=1kλi=1.

• Expected contribution: The proposed estimator is intended to reduce bias and MSE and achieve greater efficiency than existing estimators when suitable auxiliary variables are available.

Conclusion

An improved ratio-type estimator for estimating the population mean in stratified random sampling has been proposed by utilizing multiple auxiliary variables. The proposed estimator is developed based on the estimator of Kadilar and Cingi (2005), and its mean square error (MSE) is derived theoretically. The efficiency of the proposed estimator is then compared with that of the estimator proposed by Sharma and Kumar (2020) through their respective MSE expressions. The theoretical comparison demonstrates that the proposed estimator has a lower MSE than the Sharma and Kumar (2020) estimator under the considered conditions, indicating its superior efficiency. The theoretical findings are further supported by a numerical illustration based on two populations. For Population 1, the value of the existing estimator is 142.1347, whereas the proposed estimator gives a lower value of 141.4668. Similarly, for Population 2, the existing estimator has a value of 39.9800, while the proposed estimator gives 39.9000. These numerical results are consistent with the theoretical findings and demonstrate the improved performance and efficiency of the proposed estimator over the existing estimator.

References

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Copyright

Copyright © 2026 Anupama Bhadauriya, Rakesh Prasad Sarang, Gajendra Singh Rajput. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.