Ratio estimators for the population variance in simple and stratified random sampling

We propose some ratio-type variance estimators using ratio estimators for the population mean in literature. We obtain mean square error (MSE) equations of proposed estimators and show that proposed estimators are more efficient than the traditional ratio estimator, suggested by [C.T. Isaki, Variance estimation using auxiliary information, Journal of the American Statistical Association 78 (1983) 117–123], under certain conditions. We also adapt the proposed estimators in the simple random sampling to the stratified random sampling. In addition, we support the theoretical results with the aid of numerical examples. 2005 Elsevier Inc. All rights reserved.