On a new estimator for the variance of the ratio estimator with small sample corrections

The widely used formulas for the variance of the ratio estimator may lead to serious underestimates when the sample size is small; see Sukhatme (1954), Koop (1968), Rao (1969), and Cochran (1977, pages 163-164). In order to solve this classical problem, we propose in this paper new estimators for the variance and the mean square error of the ratio estimator that do not suffer from such a large negative bias. Similar estimation formulas can be derived for alternative ratio estimators as discussed in Tin (1965). We compare three mean square error estimators for the ratio estimator in a simulation study.