Efficiency comparisons for partially rank-ordered set sampling

Partially rank-ordered set sampling (PROSS) is a generalization of ranked-set sampling (RSS) in which the ranker is not required to give a full ranking in each set. In this paper, we study the efficiency of the PROSS sample mean under perfect rankings for various PROSS schemes. We obtain conditions under which one PROSS scheme is always more efficient than another, and we also obtain conditions under which how the efficiencies of two PROSS schemes compare depends on the particular distribution. We completely determine how PROSS schemes compare in the two-subset case, and we also prove a conjecture of Ozturk (Environ Ecol Stat 18:757–779, 2011) about how the efficiency of the PROSS sample mean compares to that of the RSS sample mean.

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