CDF-Based Goodness-of-Fit Tests for Ranked-Set Sampling

• Activity Number: 640
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jesse Frey*+ and Le Wang
• Companies: Villanova University and Villanova University
• Keywords: Cramer-von Mises ; Empirical distribution function ; Imperfect rankings ; Kolmogorov-Smirnov

Abstract

Parametric statistical procedures based on ranked-set sampling are sensitive both to departures from the particular parametric family and to departures from perfect rankings. In this paper, we develop goodness-of-fit tests that are sensitive to departures of both types. These tests are modeled on the familiar Kolmogorov-Smirnov and Cramer-von Mises goodness-of-fit tests for simple random sampling, and they take advantage of the fact that under perfect rankings, the cumulative distribution functions (CDFs) for the judgment order statistics are deterministic functions of the CDF for the parent distribution. We consider multiple ways of combining information across the judgment strata, and we find that summing separate stratum by stratum test statistics seems to offer the best power. We prove that the best of the proposed tests are consistent against all alternatives.