A General Class of Mean Estimators Using Mixture of Auxiliary Variables in Two-Phase Sampling in the Presence of Non-Response

Abstract

To estimate the population mean of study variable, while considering the non-response at second phase, a lot of work has been done in two-phase sampling see e.g. Khare and Srivastava (1993, 1995), Tabasum and Khan (2004), Singh and Kumar (2008) and Singh et al. (2010). Most of authors have used information of single auxiliary variable while estimating the mean of study variable, whereas in practical situation we may require/have auxiliary information on multiple characters. Khair and Sinha (2009, 2011) have used multi-auxiliary characters for estimating the population mean in the presence of non-response in the case of simple random sampling. In this paper we have suggested a general class of estimators for two-phase sampling to estimate the population mean of study variable in the case when non-response occurs at both phases and on study and auxiliary variables. Furthermore several continuous and categorical auxiliary variables have been simultaneously used while constructing the class. Also it is assumed that the information on all auxiliary variables is not available for population that is the usual case. The expressions of mean square error of suggested class have been derived and several special cases of proposed class have been identified. Empirical study has also been conducted.