Resampling Unbalanced Ranked Set Samples With Applications in Testing Hypothesis About the Population Mean

Ranked set sampling is a sampling approach that could lead to improved statistical inference when the actual measurement of the variable of interest is difficult or expensive to obtain but sampling units can be easily ordered by some means without actual quantification. In this paper, we consider the problem of bootstrapping an unbalanced ranked set sample (URSS) where the number of observations from each artificially created stratum can be unequal. We discuss resampling a URSS through transforming it into a balanced RSS and extending the existing algorithms. We propose two methods that are designed to obtain resamples from the given URSS. Algorithms are provided and several properties, including asymptotic normality of estimates, are discussed. The proposed methods are compared with the parametric bootstrap using Monte Carlo simulations for the problem of testing a hypothesis about the population mean.