Estimation of variance of the ratio estimator

Abstract

A general class of estimators of the variance of the ratio estimator is considered, which includes two standard estimators v 0 and v 2 and approximates another estimator v H suggested by Royall & Eberhardt (1975). Asymptotic expansions for the variances and biases of the proposed estimators are obtained. Based on this we obtain optimal variance estimators in the class and compare the relative merits of three estimators v 0 , v 1 and v 2 without any model assumption. Under a simple regression model a more definite comparison of v 0 , v 1 and v 2 is made in terms of variance and bias.