Quantile Inference Based on Partially Rank-Ordered Set Samples

• Activity Number: 560
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Omer Ozturk*+
• Companies: The Ohio State University
• Keywords: Imperfect ranking ; ranking models ; median confidence interval ; partially ranked set ; sign test ; judgment ranking

Abstract

In this talk, we develop statistical inference for population quantiles based on partially rank ordered set sample (PROSS) designs. The PROSS sample is similar to a ranked set sample with some clear differences. This design first creates a partially rank ordered subsets by allowing ties whenever the units in a set can not be ranked with high confidence. It then selects a unit for full measurement at random from one of these partially rank ordered subsets. Since ranking process in PROSS design utilizes full potential of rankers, it usually has a smaller ranking error than a ranked set sample of the same size. The paper develops a point estimator, confidence interval and hypothesis testing procedure for the population quantile of order $p$. Exact as well as asymptotic distribution of the test statistic is derived. It is shown that the null distribution is distribution free and statistical inference is reasonably robust against any possible ranking error in ranking process.