Variance estimation using auxiliary information: An almost unbiased multivariate ratio estimator

The goal of this paper is to investigate the repeated substitution method estimating population variance in finite population sample surveys. We propose an almost unbiased multivariate ratio estimator that has a smaller mean squared error than the conventional biased multivariate ratio estimator and with the same precision as the multivariate regression estimator. Furthermore, it is a computationally much more interesting estimator since to compute it we only need to have knowledge of correlation among available variables, which it is common to have in several practical situations. A comparison of the multi-variate ratio estimator proposed and the multivariate regression estimator is given.