Estimation of a class of population mean estimators in stratified sampling under a linear cost function

Abstract

This paper addresses the problem of estimating the population mean of the study variable using auxiliary information on an auxiliary variable in stratified random sampling. A class of transformed ratio-product type estimators is introduced, with expressions for the biases and mean squared errors (MSEs) of the proposed class of estimators derived up to the first order of approximation. Some estimators are particular members of this introduced class, and many new estimators can be generated from the suggested family of estimators. Additionally, a linear cost function is introduced, and the MSEs and optimum values for the entire family of estimators are determined. The proposed family of estimators is theoretically compared with competing estimators, and conditions under which the suggested estimators are more efficient than others are also established. An empirical study is conducted to support the suggested family of estimators. The numerical illustration demonstrated the substantial practical utility of the theoretical findings in real-world applications. The estimator with the lowest MSE is recommended for various statistical applications and for analyzing large datasets in interdisciplinary research involving statistics and data science.