Abstract
This study is devoted to obtain an ecient estima-tor for population mean in two-phase sampling using two auxiliary variables following Vishwakarma and Kumar (2014). Expressions for bias and mean squared error(MSE) are obtained to rst or-der of approximation. The new proposed estimator is compared with some competitor estimators both theoretically and numeri-cally using eight dierent data sets. It has been shown that the new proposed estimator gives more ecient results as compared to its competitor estimators.
Highlights
In sample surveys, it is common practice to use the auxiliary information either at selection stage or on estimation stage, or at both stages, to improve precision of the estimators of the population means
In case when the population mean of the auxiliary variable x is not known in advance, in such situation a first phase sample of size n is selected from the population of size N and only the auxiliary variable x is measured to get an estimate of population mean X
Following Vishwakarma and Kumar (2014), we suggest a class of estimators for the population mean in two-phase sampling using two auxiliary variables
Summary
It is common practice to use the auxiliary information either at selection stage or on estimation stage, or at both stages, to improve precision of the estimators of the population means. Prasad et al (1996), Singh and Espejo (2007), Singh and Choudhury (2012), Vishwakarma and Gangele (2014) and several authors have proposed some improved chain ratio, product and regression type estimators in two-phase sampling based on two auxiliary variables. Singh and Choudhury (2012) suggested exponential chain type ratio estimator of Y under two-phase sampling scheme using two auxiliary variables x and z , is given by yRde exp x z. Singh and Choudhury (2012) suggested exponential chain type product estimator of Y under two-phase sampling scheme using two auxiliary variables x and z , is given by yPde y exp x z x z (11). Vishwakarma and Kumar (2014) suggested exponential chain ratio- product type estimator of Y under two-phase sampling scheme using two auxiliary variables x and z , is given by yd RP e. The minimum bias and of y d RPe at optimum value of i.e
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