A Ratio Estimator Under General Sampling Design

Abstract

Recently, many authors introduced ratio-type estimators for estimating the mean, or the ratio, for a finite populations. Most of the articles are discussing this problem under simple random sampling design, with more assumptions on the auxiliary variable such as the coefficient of variation, and kurtosis are assumed to be known. Gupta and Shabbir (2008) have suggested an alternative form of ratio-type estimators and they assumed the coefficient of variation of the auxiliary variable must be known; this assumption is crucialfor this estimator.An estimator of the population ratio, under general sampling design, is proposed.Further, exact and an unbiased variance estimator of this estimator are obtained, and the Godambe-Joshi lower bound is asymptotically attainable for this estimator. The assumption on the coefficient of variation of the auxiliary variable is not needed for the proposed estimator. Simulation results from real data set and simulations from artificial population, show that the performance of the proposed estimator is better than Gupta and Shabbir (2008) and Hartley and Ross (1954) estimators.