An improved family of estimators for estimating population mean using a transformed auxiliary variable under double sampling

The performance of a population mean estimator can be improved by transformation techniques using a subset of the population data. An improved family of estimators for population mean has been proposed under double sampling using a transformed auxiliary variable. The biases and mean square errors of the proposed family of estimators up to the first order of approximation have been investigated. Simulation studies and an application to fine particulate matter in Chiang Rai, Thailand, are used to study the efficiency of the proposed estimators. The results from an application to air pollution in Chiang Rai showed that the proposed estimators gave smaller biases, by at least a half of the existing ones, and gave at least four times less mean square error than the existing ones.