Unbalanced Ranked Set Sampling in CRDs and Its Application to Missing Data from Balanced Design

• Activity Number: 303 - Recent Developments on Order-Related Designs and Inferences
• Type: Topic Contributed
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Korean International Statistical Society
• Author(s): Soohyun Ahn* and Xinlei (Sherry) Wang and Johan Lim
• Companies: Ajou University and Southern Methodist University and Seoul National University
• Keywords: Hierarchical linear models; Missing data; Neyman allocation; Order statistics; Ranking error; Relative efficiency

Abstract

We consider the use of unbalanced ranked set sampling (URSS) with cluster randomized designs (CRDs), and extend nonparametric estimators and testing methods, previously developed by Wang et al. (2016) for the use of balanced RSS (BRSS) with CRDs, to account for unbalanced stratified structures under different ranking schemes. We study the optimality, finite-sample and asymptotic properties of the URSS estimators, and numerically quantify and compare the relative efficiency of the URSS vs. BRSS estimators. We also study and compare the power of the URSS tests vs. their BRSS counterparts via simulation. Further, we investigate the application of the proposed methods to unbalanced data from BRSSstructured CRDs due to missing observations and illustrate it with an example using educational data.