An Efficient Class of Chain Estimators of Population Variance under Sub-Sampling Scheme

For estimating the population variance S2y of study variable y, a class of chain estimators of S2y has been proposed in the presence of two auxiliary variables x and z by using known information on population mean and variance of the second auxiliary variable z. In this proposed class, the second auxiliary variable z is directly highly correlated with the first auxiliary variable x, whereas the variable z is correlated with the variable y due to only the high correlation between the variables y and x. Another generalized class of estimators of S2y has also been considered by using the same available information of auxiliary variable z when both the auxiliary variables x and z are directly highly correlated with the study variable y. The asymptotic expressions for the mean square errors and their optimum values have been obtained. A comparison between the two proposed classes of estimators of S2y has been made empirically.