Unbiased and almost unbiased ratio estimators of the population mean in ranked set sampling

Abstract

In this paper we study the problem of reducing the bias of the ratio estimator of the population mean in a ranked set sampling (RSS) design. We first propose a jackknifed RSS-ratio estimator and then introduce a class of almost unbiased RSS-ratio estimators of the population mean. We also present an unbiased RSS-ratio estimator of the mean using the idea of Hartley and Ross (Nature 174:270–271, 1954) which performs better than its counterpart with simple random sample data. We show that under certain conditions the proposed unbiased and almost unbiased RSS-ratio estimators perform better than the commonly used (biased) RSS-ratio estimator in estimating the population mean in terms of the mean square error. The theoretical results are augmented by a simulation study using a wheat yield data set from the Iranian Ministry of Agriculture to demonstrate the practical benefits of our proposed ratio-type estimators relative to the RSS-ratio estimator in reducing the bias in estimating the average wheat production.