Robust Confidence Intervals for a Proportion Using Ranked-Set Sampling

• 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): Yimin Zhang* and Jesse Frey
• Companies: Villanova University and Villanova University
• Keywords: Clopper-Pearson; Imperfect rankings; Maximum likelihood estimation; Mid-P adjustment

Abstract

We develop two new approximate confidence interval methods for estimating a population proportion using ranked-set sampling (RSS). Unlike existing RSS-based methods, the new methods control the coverage probability well not just under perfect rankings, but also under imperfect rankings. One method uses a Wilson-type interval, and the other is based on making a mid-P adjustment to a Clopper Pearson-type interval. Both methods rely on a new maximum-likelihood-based method for estimating the proportions in the judgment strata when the overall proportion is given, and both can be computed even for large sample sizes.