Estimation of Finite Population Mean Using Partially Ordered Set Samples

• 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): Omer Ozturk*+
• Companies: The Ohio State University
• Keywords: Inclusion probabilities ; Ranked set sampling ; Horwitz-Thompson estimator ; Bootstrap confidence interval ; Judgment ranking ; Auxiliary variables

Abstract

This paper introduces three finite population sampling designs. The proposed sampling designs select sets of sampling units. Units in these sets are judgment ranked by all available raters without a measurement. Ranking process allows ties among ranks whenever units cannot be ranked accurately with high confidence. Ranking information of all raters is combined in a meaningful way to construct a strength-of-agreement weight. These weights are then used to select a single sampling unit for a full measurement in each set. The sample can be constructed with three levels of "without replacement" policies, level-0, level-1 and level-2. Level-0 sample is constructed with replacement policy, level-1 sample is constructed without replacement policy of the fully measured unit in each ranking group, and level-2 sample is constructed without replacement policy of the entire set in each ranking group. For these sampling designs, we compute the first and second order inclusion probabilities and construct estimators for the population total, mean and variance. We show that the new sampling designs provide substantial amount of efficiency gain over their competitor estimators in the literature.