Bounds on the efficiency of unbalanced ranked-set sampling

Jesse Frey

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 1, 243-256

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 on the set size and is achieved for uniform distributions. Here we generalize the Takahasi and Wakimoto (1968) result by finding a sharp upper bound in the case of unbalanced RSS. The bound depends on the particular unbalanced design, and the distributions where the bound is achieved can be highly nonuniform. The bound under perfect rankings can be exceeded under imperfect rankings.

Date: 2020
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DOI: 10.1080/03610926.2018.1543769

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