Bounds on the Efficiency of Unbalanced Ranked-Set Sampling

• Activity Number: 346 - Recent Advances in Nonparametric Statistical Methods
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jesse Frey*
• Companies: Villanova University
• Keywords: Calculus of variations; Imperfect rankings; Quantile function; Ranked-set sampling

Abstract

Takahasi and Wakimoto (1968) derived a sharp upper bound on the efficiency of the balanced ranked-set sampling (RSS) sample mean relative to the simple random sampling (SRS) sample mean under perfect rankings. The bound depends only on the set size, and it is achieved when the parent distribution is uniform. Here we generalize the Takahasi and Wakimoto (1968) result by finding a sharp upper bound on the efficiency of the unbalanced RSS sample mean relative to the SRS sample mean. The bound depends on the vector of in-stratum sample sizes, and the distributions where the bound is achieved can be highly nonuniform. We also consider what happens under imperfect rankings, showing that there are cases where the maximum efficiency under imperfect rankings can be far higher than the maximum efficiency under perfect rankings.