Estimating population characteristics by incorporating prior values in stratified random sampling/ranked set sampling

In this paper, we discuss the estimation of population characteristics using stratified random sampling in an infinite population framework, including ranked set sampling as a special case. The use of prior values is considered and the underlying distribution is assumed to be unknown. The estimator considered in each stratum is the weighted mean of the U-statistic and prior value. The optimum weight is obtained by minimizing the mean squared error of the estimator of the population characteristics, but it contains unknown parameters and those parameters are replaced with their estimates. Simulation results show the gains in efficiency of the proposed estimator, yielding gains of at least 1.2 times larger than the usual unbiased estimator under certain condition specified in the text. Guidelines for the usage of the proposed estimator are shown and an application to a real data set is provided.