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Optimal sign tests for data from ranked set samples

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  • Wang, You-Gan
  • Zhu, Min

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.

Suggested Citation

  • Wang, You-Gan & Zhu, Min, 2005. "Optimal sign tests for data from ranked set samples," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 13-22, April.
    • Handle: RePEc:eee:stapro:v:72:y:2005:i:1:p:13-22
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    References listed on IDEAS

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    1. Öztürk, Ömer & Wolfe, Douglas A., 2000. "Alternative ranked set sampling protocols for the sign test," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 15-23, March.
    2. You-Gan Wang & Zehua Chen & Jianbin Liu, 2004. "General Ranked Set Sampling with Cost Considerations," Biometrics, The International Biometric Society, vol. 60(2), pages 556-561, June.
    3. Hassen Muttlak, 2001. "Regression estimators in extreme and median ranked set samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(8), pages 1003-1017.
    4. 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, May.
    5. Vic Barnett & Karen Moore, 1997. "Best linear unbiased estimates in ranked-set sampling with particular reference to imperfect ordering," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(6), pages 697-710.
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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, vol. 85(C), pages 69-77.

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