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Constrained nonparametric estimation of the mean and the CDF using ranked-set sampling with a covariate

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Abstract

Ranked-set sampling (RSS) and judgment post-stratification (JPS) are related schemes in which more efficient statistical inference is obtained by creating a stratification based on ranking information. The rankings may be completely subjective, or they may be based on values of a covariate. Recent work has shown that regardless of how the rankings are done, the in-stratum cumulative distribution functions (CDFs) must satisfy certain constraints, and we show here that if the rankings are done according to a covariate, then tighter constraints must hold. We also show that under a mild stochastic ordering assumption, still tighter constraints must hold. Taking advantage of these new constraints leads to improved small-sample estimates of the in-stratum CDFs in all RSS and JPS settings. For JPS, the new constraints also lead to improved estimates of the overall CDF and the population mean.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Villanova University, Villanova, PA, 19085, USA

    Jesse Frey

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  1. Jesse Frey
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Correspondence to Jesse Frey.

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Frey, J. Constrained nonparametric estimation of the mean and the CDF using ranked-set sampling with a covariate. Ann Inst Stat Math 64, 439–456 (2012). https://doi.org/10.1007/s10463-011-0326-9

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  • DOI: https://doi.org/10.1007/s10463-011-0326-9

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