Calibration Ratio Estimator for Estimating Population Mean in Stratified Random Sampling Design Using Properties of Two Supplementary Variables

Etebong Clement¹ , Idorenyin Etukudoh²

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.5 , pp.14-21, Oct-2023

Online published on Oct 31, 2023

Copyright © Etebong Clement, Idorenyin Etukudoh . 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.
 

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Abstract :
The performances of most improved ratio estimators may depend on some optimality conditions. This study introduced calibration weightings that produce more efficient ratio estimator that is independent on any optimality conditions. Calibration ratio estimator for estimating population mean when two auxiliary variables are available is proposed under the stratified random sampling design. The bias and mean square error expressions for the proposed estimator are formulated using the principle of large sample approximation. The method was adopted to guarantee optimal performances of the proposed estimator in terms of minimum mean square error and efficient bias reduction. Analytical and numerical illustrations were carried out to compare the performances of the proposed estimator with existing ratio and regression-type estimators of population mean under study. Analytically, the proposed estimator under certain prescribed conditions has been showed to perform better than all existing estimators under review. The numerical results also showed that the proposed estimator is substantially superior in terms of efficiency to all existing estimators under study including the classical multivariate regression estimator of population mean by Cochran [31]. This is against an established fact in survey sampling literature that generally the regression estimator is more efficient than the ratio and product estimators of population mean. Analysis and evaluation are presented.

Key-Words / Index Term :
Bias reduction, calibration weightings, efficiency, mean square error, ratio estimation

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