An Improved Exponential Ratio-Type Estimator in Double Sampling Under Partial Nonresponse

Abstract

This study proposed an improved ratio-type estimator for estimating the population mean in a double sampling framework under partial nonresponse on both study and auxiliary variables. The proposed estimator utilized information from two auxiliary variables to improve estimation efficiency and mitigate the adverse effects of nonresponse. The theoretical properties of the estimator, including bias and mean square error (MSE), were derived up to the first order of approximation and underlying conditions for optimal performance establishing the superiority of the proposed estimator over existing methods established. An empirical study using real dataset was performed and the results demonstrated that the proposed estimator consistently achieved lowest MSE, lowest CV and highest relative efficiency (RE). The findings revealed that incorporating dual auxiliary information within a double sampling scheme significantly enhances estimation accuracy in the presence of partial nonresponse. The proposed estimator is therefore recommended for practical applications in survey sampling where nonresponse occurs on both study and auxiliary variables in double sampling.