A wide and efficient class of estimators of population variance under sub-sampling scheme

Abstract

Here, it is assumed that the prior information on the parameters of first auxiliary variable x is not available, but the prior information on the parameters of second auxiliary variable z is available for improving the estimators of parameters of interest. We consider the situation when the auxiliary variable x is directly and highly correlated with both the study variable y and the second auxiliary variable z. In this paper, we propose a class of estimators of population variance ${\mathit{S}}_{\mathit{y}}^2$ of a study variable y when the population mean and variance of an auxiliary variable z are known in advance. We compare efficiency of various classes of estimators of ${\mathit{S}}_{\mathit{y}}^2$ . It has been shown that the proposed class is wider and more efficient than the two existing classes defined by Jhajj et al. (J Japan Stat Soc 35(2) (2005), 273–286) even though the same prior information about the second auxiliary variable z is used in all the classes.