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Optimal sign tests for data from ranked set samples

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  • Wang, You-Gan
  • Zhu, Min
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    Abstract

    This paper considers the one-sample sign test for data obtained from general ranked set sampling when the number of observations for each rank are not necessarily the same, and proposes a weighted sign test because observations with different ranks are not identically distributed. The optimal weight for each observation is distribution free and only depends on its associated rank. It is shown analytically that (1) the weighted version always improves the Pitman efficiency for all distributions; and (2) the optimal design is to select the median from each ranked set.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 72 (2005)
    Issue (Month): 1 (April)
    Pages: 13-22

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    Handle: RePEc:eee:stapro:v:72:y:2005:i:1:p:13-22

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    Related research

    Keywords: Nonparametric Pitman efficiency Ranked set sampling Sign tests;

    References

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    1. Steven N. MacEachern & Ömer Öztürk & Douglas A. Wolfe & Gregory V. Stark, 2002. "A new ranked set sample estimator of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 177-188.
    2. Öztürk, Ömer & Wolfe, Douglas A., 2000. "Alternative ranked set sampling protocols for the sign test," Statistics & Probability Letters, Elsevier, Elsevier, vol. 47(1), pages 15-23, March.
    3. Hassen Muttlak, 2001. "Regression estimators in extreme and median ranked set samples," Journal of Applied Statistics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 28(8), pages 1003-1017.
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    Cited by:
    1. Zhang, Liangyong & Dong, Xiaofang & Xu, Xingzhong, 2014. "Sign tests using ranked set sampling with unequal set sizes," Statistics & Probability Letters, Elsevier, Elsevier, vol. 85(C), pages 69-77.

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