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On the evaluation of the joint distribution of order statistics

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  • Kwong, Koon-Shing
  • Chan, Yiu-Man

Abstract

Dunnett and Tamhane [Dunnett, C.W., Tamhane, A.C., 1992. A step-up multiple test procedure. J. Amer. Statist. Assoc. 87, 162-170.] proposed a step-up procedure for comparing k treatments with a control and showed that the step-up procedure is more powerful than its counterpart single step and step-down procedures. Since then, several modified step-up procedures have been suggested to deal with different testing environments. In order to establish those step-up procedures, it is necessary to derive approaches for evaluating the joint distribution of the order statistics. In some cases, experimenters may have difficulty in applying those step-up procedures in multiple hypothesis testing because of the computational limitation of existing algorithms in evaluating the critical values for a large number of multiple comparisons. As a result, most procedures are only workable when the design of the experiment is balanced with k

Suggested Citation

  • Kwong, Koon-Shing & Chan, Yiu-Man, 2008. "On the evaluation of the joint distribution of order statistics," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5091-5099, August.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5091-5099
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    References listed on IDEAS

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    1. Koon Shing Kwong & Siu Hung Cheung & Wai Sum Chan, 2004. "Multiple Testing to Establish Superiority/Equivalence of a New Treatment Compared with k Standard Treatments for Unbalanced Designs," Biometrics, The International Biometric Society, vol. 60(2), pages 491-498, June.
    2. Koon-Shing Kwong, 2001. "An algorithm for construction of multiple hypothesis testing," Computational Statistics, Springer, vol. 16(1), pages 165-171, March.
    3. Kwong, K. S. & Liu, W., 2000. "Calculation of critical values for Dunnett and Tamhane's step-up multiple test procedure," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 411-416, October.
    4. H. Finner & M. Roters, 1994. "On the limit behaviour of the joint distribution function of order statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 343-349, June.
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    Cited by:

    1. Kwong, Koon Shing & Cheung, Siu Hung, 2012. "Optimal design for p-value consistent step-up procedures for multiple comparisons with a control in direction-mixed families," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4157-4164.

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