Title: Proportion estimation in ranked set sampling in the presence of tie information
Authors: Ehsan Zamanzade - University of Isfahan (Iran)
Xinlei Wang - Southern Methodist University (United States)
Xinlei Wang - Southern Methodist University (United States) [presenting]
Abstract: Ranked set sampling (RSS) is a statistical technique that uses auxiliary ranking information of unmeasured sample units in an attempt to select a more representative sample that provides better estimation of population parameters than simple random sampling (SRS). However, the use of RSS can be hampered by the fact that a complete ranking of units in each set must be specified when implementing RSS. Recently, to allow ties declared as needed, a modification of RSS has been proposed, which is to simply break ties at random so that a standard ranked set sample is obtained, and meanwhile record the tie structure for use in estimation. Under this RSS variation, several mean estimators were developed and their performance was compared via simulation, with a focus on continuous outcome variables. We extend that to binary outcomes and investigate three nonparametric and three likelihood-based proportion estimators (with/without utilizing tie information), among which four are directly extended from existing estimators and the other two are novel. Under different tie-generating mechanisms, we compare the performance of these estimators and draw conclusions based on both simulation and a data example of breast cancer prevalence. Suggestions are made about the choice of the proportion estimator in general.