A generalized class of estimators for the mean using multiauxiliary information in adaptive cluster sampling

Abstract

This article addresses the problem of estimating the population mean of variable y using information from multiple auxiliary variables in adaptive cluster sampling. We define a class of estimators based on p(>1) auxiliary variables derive bias and mean squared error expressions up to order n−1, and determine optimal conditions for minimizing mean squared error. Our findings demonstrate that the proposed estimators outperform the multiple linear regression estimator. We also identify several existing estimators as members of this class, including those introduced by Dryver and Chao (2007), Chutiman and Kumphon (2008), Chutiman (2013), Chaudhry (2014), Chaudhry and Hanif (2015), and Yadav et al. (2016). Furthermore, we obtain the correct values of constants “a” and “b” for the Chaudhry and Hanif (2015) estimator, leading to an accurate expression for its minimum mean squared error. To assess the performance of these estimators, we conduct a simulation study.