Constrained Nonparametric Estimation Using Ranked-Set Sampling with a Covariate

• Activity Number: 339
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jesse Frey*+
• Companies: Villanova University
• Keywords: Concomitant ; Convexity ; Judgment post-stratification ; Maximum likelihood estimation ; Stratified sampling ; Woodruff confidence intervals

Abstract

Ranked-set sampling and judgment post-stratification are related schemes in which more efficient statistical inference is obtained by creating a stratification based on ranking information. The rankings that are used may be completely subjective, or they may be based on values of a covariate. Recent work has shown that regardless of how the rankings are done, the in-stratum cumulative distribution functions (CDFs) must satisfy certain constraints, and these constraints may be used to obtain better estimates of the in-stratum CDFs, the overall CDF, and the population mean. We show here that if the rankings are done according to a covariate, then tighter constraints must hold. We also show that under a mild stochastic ordering assumption, still tighter constraints must hold. Taking advantage of these new constraints leads to improved estimation of key population parameters.