Unbalanced Ranked Set Sampling for Estimating A Population Proportion Under Imperfect Rankings
The application of unbalanced ranked set sampling (RSS) to estimation of a population proportion has been studied for the perfect ranking situation. When the rankings are not perfect, the probabilities of success ranks for the judgment order statistics incorporate information on ranking errors as well as ranks. The objective of this article is to investigate the ranking errors effect of imperfection in rankings on unbalanced RSS for binary variables and provide methods to obtain estimates for the probabilities of success for the judgment order statistics using training samples so that Neyman allocation can be implemented. We also use a substantial data set, the NHANES III data, to demonstrate the feasibility and benefits of Neyman allocation in RSS for binary variables in the case of imperfect rankings.