Statistical Inference Based on Expanded Simple Random Sample Using Population Ranks

• Activity Number: 617 - Recent Developments on Order-Related Designs and Inferences
• Type: Topic Contributed
• Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Omer Ozturk*
• Companies: Ohio State University
• Keywords: Subsample ; Ranked set sample ; Judgment post stratified sample ; Finite population ; Order statistics ; Ranking error

Abstract

In this paper, we consider a population for which ranks of population units are available. We first identify N units without measurement form this population and determine their ranks. From these N identified units, we construct a simple random sample of size n (n < N) without replacement and measure all of them. We expand this simple random sample to size M (N>M >n-1)) by inserting (M-n) additional units selected at random from the remaining unmeasured N-n units in the population. We now compute the probability distribution of the ranks of measured units in the expanded sample by conditioning on their ranks among N unmeasured units. The final sample contains n measured units and conditional distribution of their ranks in the expanded sample. We construct an estimator for the population mean and show that it has substantial amount of improvement in efficiency over its competitors.