Environmental and Ecological Statistics

, Volume 13, Issue 1, pp 25–40

Nonparametric Ranked-set Sampling Confidence Intervals for Quantiles of a Finite Population

Original Article

DOI: 10.1007/s10651-005-5688-9

Cite this article as:
Deshpande, J.V., Frey, J. & Ozturk, O. Environ Ecol Stat (2006) 13: 25. doi:10.1007/s10651-005-5688-9

Abstract

Ranked-set sampling from a finite population is considered in this paper. Three sampling protocols are described, and procedures for constructing nonparametric confidence intervals for a population quantile are developed. Algorithms for computing coverage probabilities for these confidence intervals are presented, and the use of interpolated confidence intervals is recommended as a means to approximately achieve coverage probabilities that cannot be achieved exactly. A simulation study based on finite populations of sizes 20, 30, 40, and 50 shows that the three sampling protocols follow a strict ordering in terms of the average lengths of the confidence intervals they produce. This study also shows that all three ranked-set sampling protocols tend to produce confidence intervals shorter than those produced by simple random sampling, with the difference being substantial for two of the protocols. The interpolated confidence intervals are shown to achieve coverage probabilities quite close to their nominal levels. Rankings done according to a highly correlated concomitant variable are shown to reduce the level of the confidence intervals only minimally. An example to illustrate the construction of confidence intervals according to this methodology is provided.

Keywords

Order statistics Interpolated confidence intervals Median Efficiency Sampling designs 

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of StatisticsThe Ohio State UniversityColumbusUSA

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