Optimal Strategy for Elevated Estimation of Population Mean in Stratified Random Sampling under Linear Cost Function

Subhash Kumar Yadav (), Mukesh Kumar Verma () and Rahul Varshney ()
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Subhash Kumar Yadav: Babasaheb Bhimrao Ambedkar University
Mukesh Kumar Verma: Babasaheb Bhimrao Ambedkar University
Rahul Varshney: Babasaheb Bhimrao Ambedkar University

Annals of Data Science, 2025, vol. 12, issue 2, No 5, 517-538

Abstract: Abstract In this paper, we propose the exponential ratio-type estimator for the elevated estimation of population mean, implying one auxiliary variable in stratified random sampling using the conventional ratio and, Bahl and Tuteja exponential ratio-type estimators. The bias and the Mean Squared Error (MSE) of the proposed estimator are derived up to a first-order approximation and compared with existing estimators. Theoretically, we also compare MSE of the proposed estimator using the linear cost function with the competing estimators. The optimal values of the characterizing scalars are obtained and for these optimal values of characterizing scalars, the minimum MSE is obtained. We find theoretically that the proposed estimator is more efficient than other estimators under restricted conditions by formulating the proposed problem as an optimization problem under linear cost function. The numerical illustration is also included to verify theoretical findings for their practical utility. The estimator with least MSE is recommended for practical utility in different areas of applications of stratified random sampling.

Keywords: Study variable; Auxiliary variable; Bias; MSE; PRE and linear cost function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s40745-024-00520-9

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