Unbiased and almost unbiased ratio estimators of the population mean in ranked set sampling
Jozani, M.J.; Majidi, S.; Perron, F.
Statistical Papers 53(3): 719-737
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.