A minimum variance unbiased estimator of finite population variance using auxiliary information

A class of estimators of finite population variance (S_y^2) using auxiliary information has been proposed under simple random sampling without replacement (SRSWOR) scheme. An attempt has been made to derive the minimum variance unbiased estimator of finite population variance from the proposed class of unbiased estimators. The efficiency of the class of estimators under optimality is compared with the usual unbiased estimator (t_{V0}=s_y^2), ratio type estimator (t_{VR}), product type estimator{\ (t}_{VP}), regression type estimator {(t}_{Vlr}), exponential ratio type estimator{\ (t}_{VER}), exponential product type estimator {\ (t}_{VEP}), and ratio-in-regression estimator (t_s), both theoretically and empirically under general conditions and under bivariate normality. The proposed class of estimator performs better than these estimators under certain realistic conditions. The proposed class of estimators is generalized for the case of multi-auxiliary variables.