A class of estimators of the population mean in survey sampling using auxiliary information

For estimating the mean of a finite population using information on an auxiliary variable, a class of estimators is defined as a function of the ratio of sample mean to population mean and the ratio of sample variance to population variance of the auxiliary variable. Asymptotic expressions for bias and mean squared error are obtained. A condition is given for the minimum mean squared error of estimators of this class to be smaller than those which use only the ratio of sample mean to population mean of the auxiliary variable.