Logarithmic Estimators in Small Area for Estimation of Population Mean

Small area estimation is a branch of statistical science that integrates survey sampling, statistical models, and inference about a finite population. The necessity for small area estimating approaches has also emerged as a result of agricultural development planning for rapid production increase, etc. For improved estimates and to increase the accuracy of the estimators, information from an auxiliary variable that is highly associated with the variable under study may be readily available. As a result, sample surveys frequently use auxiliary information to estimate parameters of interest in small areas. Numerous researchers have suggested a wide range of estimators using various methodologies. This study aims to provide logarithmic type estimators for small areas that estimate the population mean for straightforward random sampling techniques using data on a single auxiliary variable. For the logarithmic estimators, the bias and mean square error have been computed. Proposed estimators are shown to be more effective than other widely used estimators in specific real-world settings. The fact that these estimators reduce to regression estimators is also shown. To demonstrate the proposed estimators' superiority over other exciting estimators, numerical results of their efficiency are shown as percent relative efficiencies (PRE).