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THE OPTIMAL RANKED-SET SAMPLING SCHEME FOR INFERENCE ON POPULATION QUANTILES

Zehua Chen
Statistica Sinica
Vol. 11, No. 1 (January 2001), pp. 23-37
Stable URL: http://www.jstor.org/stable/24306807
Page Count: 15
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
THE OPTIMAL RANKED-SET SAMPLING SCHEME FOR INFERENCE ON POPULATION QUANTILES
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Abstract

In this article, we consider the design of unbalanced ranked-set sampling in order to achieve certain optimality for inference on quantiles. We first derive the asymptotic properties of the unbalanced ranked-set sample quantiles for any unbalanced ranked-set sampling scheme. Then these properties are employed to develop a methodology for determining optimal ranked-set sampling schemes. In the case of inference on a single quantile, the optimal scheme results in an estimator of the quantile which is asymptotically unbiased and with minimum variance among all ranked-set sample (balanced or unbalanced) quantiles. The striking feature of the methodology is that it is distribution-free. The optimal schemes for inference on certain quantiles are computed. Some simulation studies are reported.

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