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Finding the maximum efficiency for multistage ranked-set sampling

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  • Jesse Frey
  • Timothy G. Feeman

Abstract

Multistage ranked-set sampling (MRSS) is a generalization of ranked-set sampling in which multiple stages of ranking are used. It is known that for a fixed distribution under perfect rankings, each additional stage provides a gain in efficiency when estimating the population mean. However, the maximum possible efficiency for the MRSS sample mean relative to the simple random sampling sample mean has not previously been determined. In this paper, we provide a method for computing this maximum possible efficiency under perfect rankings for any choice of the set size and the number of stages. The maximum efficiency tends to infinity as the number of stages increases, and, for large numbers of stages, the efficiency-maximizing distributions are symmetric multi-modal distributions where the number of modes matches the set size. The results in this paper correct earlier assertions in the literature that the maximum efficiency is bounded and that it is achieved when the distribution is uniform.

Suggested Citation

  • Jesse Frey & Timothy G. Feeman, 2018. "Finding the maximum efficiency for multistage ranked-set sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(17), pages 4131-4141, September.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:17:p:4131-4141
    DOI: 10.1080/03610926.2017.1367816
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    Cited by:

    1. M. Mahdizadeh & Ehsan Zamanzade, 2021. "Smooth estimation of the area under the ROC curve in multistage ranked set sampling," Statistical Papers, Springer, vol. 62(4), pages 1753-1776, August.

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