GENERALIZED CLASS OF MEAN ESTIMATORS FOR TWO PHASE SAMPLING IN THE PRESENCE OF NONRESPONSE

A lot of work has been done in two-phase sampling for estimating the population mean of a study variable while considering the non-response at the second phase, see e.g. Khare and Srivastava (1993, 1995), Tabasum and Khan (2004), Singh and Kumar (2008) and Singh et al. (2010). Most authors have used information of a single auxiliary variable while estimating the mean of the study variable, whereas in a practical situation we may require/have auxiliary information on multiple characters. Khare and Sinha (2009, 2011) have used multi-auxiliary characters to estimate the population mean in the presence of nonresponse in the case of simple random sampling. In two-phase sampling, when auxiliary information is obtained at both phases, the nonresponse may occur at both phases as well. In this paper we have proposed a generalized class of estimators for estimating the population mean of a study variable under a two-phase sampling scheme using multi-auxiliary variable(s) in the presence of nonresponse at both phases. The information on all auxiliary variable(s) is not known for the population. The bias and mean square error have been derived for the suggested class. Special cases of the class have also been identified. An empirical study has been conducted for comparing the efficiency of the proposed estimators with a modified version of existing ones.