Bootstrap Confidence Bands for the CDF Using Ranked-Set Sampling

• Activity Number: 280
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jesse Frey*+
• Companies: Villanova University
• Keywords: Exact bootstrap ; Imperfect rankings ; Kolmogorov-Smirnov ; Stratified random sampling

Abstract

In ranked-set sampling, a stratification by ranks is used to obtain a sample that tends to be more informative than a simple random sample of the same size. Previous work has shown that if the rankings are perfectly accurate, then one can obtain confidence bands for the CDF that are narrower than those obtained under simple random sampling. Here we develop confidence bands that work well even when the rankings are not perfect. These confidence bands are obtained by using a smoothed bootstrap procedure that takes advantage of special features of ranked-set sampling. We show that the coverage probabilities are close to nominal even for samples with just two or three observations. A new computational algorithm allows us to avoid the bootstrap simulation step when sample sizes are relatively small.