Generalized Hartley–Ross Unbiased Ratio-Type Estimator

Abstract

RATIO method of estimation is frequently used in sample surveys to estimate the population mean of the variable under investigation. Several ratio-type estimates can be formed. All these estimates are unsatisfactory in the sense that they are biased. This difficulty was overcome by Hartley and Ross¹, who proposed an unbiased ratio-type estimator for uni-stage sampling designs. In practice, however, we are generally faced with multi-stage sampling designs. This communication gives a generalized form of Hartley–Ross unbiased ratio-type estimator for multi-stage designs. Let N = number of first-stage units in the population, M = number of second-stage units in each of the first-stage units, P = number of third-stage units in each of the second-stage units, Yijk = the value of the variable under investigations for the k-th unit in the j-th second-stage unit of the i-th first-stage unit, and