In this article, we propose some direct and synthetic logarithmic estimators for estimating the domain mean of small area based on a simple random sampling design. The mean square error expressions of the proposed direct and synthetic estimators are obtained to first order approximation. The efficiency conditions are obtained under which the proposed direct and synthetic estimators dominate their conventional aspirants. The performances of the suggested direct and synthetic logarithmic estimators are examined by a comprehensive simulation study carried out on some artificially drawn symmetric and asymmetric populations. Furthermore, a real data application of the suggested methods is also provided as a case study using the paddy crop acreage data for small domains, where small domains are the revenue inspector circles (RIC) in Mohanlalganj tehsil, Uttar Pradesh, India.

Small area estimation using design based direct and synthetic logarithmic estimators