Use of auxiliary information in estimation of the finite population mean: An exponential type of estimator

Abstract

The use of auxiliary information has a long history in statistical theory and estimation procedures. The utility of supplementary knowledge becomes vital when information about the study variable is limited. In this paper, we present a more competent mechanism to utilise auxiliary information in the estimation of the finite population mean. We propose a new exponential type of estimator for the estimation of finite population mean in the scenario where a simple random sampling scheme is adopted. Our proposed procedure is based on the dual use of the supportive information to maximise additional gain and involves the use of the mean of the auxiliary variable along with its rank to increase the extent of relevant information. The comparative performance of the proposed scheme is demonstrated with respect to 10 most used, classic, and some recent procedures in estimation theory literature. These are the classic mean estimator 𝑌 ̅ ̂𝑠𝑟𝑠 , the so-called traditional ratio, product, and regression estimators 𝑌 ̅ ̂𝑅, 𝑌 ̅ ̂𝑃 and 𝑌 ̅ ̂𝑟𝑒𝑔 , respectively, along with the difference type estimator 𝑅.𝐷 . In addition, the more recent estimators investigated are the ratio-product exponential type 𝑌 ̅ ̂𝑆,𝑅𝑃 , difference exponential type 𝑌 ̅ ̂𝐺𝐾 , ratio exponential 𝑌 ̅ ̂𝐵𝑇,𝑅 , product exponential 𝑌 ̅ ̂𝐵𝑇,𝑃 and the ratio-product-exponential 𝑌 ̅ ̂𝑆𝐻𝐺 , all used for comparison. Moreover, we consider three data sets of a multi-disciplinary nature, encompassing health surveillance, industrial production and poultry. The choice of data sets is mainly motivated by two reasons; (i) these data sets have been topics of contemporary techniques and, (ii) the considered data sets do offer a wide range of parametric settings, including lower extent of correlation between the study variable with the auxiliary variable and they also vary in sample sizes.