Calibration approach-based chain ratio type and chain product type estimators in two-phase sampling involving two auxiliary variables

Abstract

In this article, we propose a chain ratio type and a chain product type estimator of population total in two-phase sampling when information on two auxiliary characters is available in different phases. It is assumed that complete information is available for one auxiliary variable while information is not available for the other auxiliary variable, assumed highly correlated with the study variable, and the double sampling approach is proposed accordingly. Two cases are considered: (i) both the auxiliary variables are positively correlated with the study variable and (ii) both the auxiliary variables are negatively correlated with the study variable. Expressions for the bias and the mean square error of proposed estimators have been obtained, and also their estimators. It is shown, through empirical studies, that the proposed estimators perform better than existing estimators in terms of the criteria of relative bias, Monte Carlo relative efficiency, and percentage relative gain.