*J. Japan Statist. Soc.,* Vol. 35 (No. 2), pp. 273-286, 2005

## An Efficient Class Of Chain Estimators of Population Variance Under Sub-Sampling Scheme

H. S. Jhajj, M. K. Sharma and Lovleen Kumar Grover

**Abstract. **
For estimating the population variance *S*_{y}^{2} of study variable *y*, a class of chain estimators of *S*_{y}^{2} 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 *S*_{y}^{2} 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 *S*_{y}^{2} has been made empirically.

*Key words and phrases*:
Auxiliary variable, chain estimator, consistent estimator, double sampling technique, mean square error, optimum estimator, study variable.

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