IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v58y2017i3d10.1007_s00362-015-0725-8.html
   My bibliography  Save this article

On the Simes test under dependence

Author

Listed:
  • H. Finner

    (Leibniz Institute for Diabetes Research at Heinrich-Heine-University Düsseldorf)

  • M. Roters

    (Universität Trier)

  • K. Strassburger

    (Leibniz Institute for Diabetes Research at Heinrich-Heine-University Düsseldorf)

Abstract

In 1986, R. J. Simes proposed a modified Bonferroni test procedure for testing an overall null hypothesis in multiple testing problems, nowadays referred to as the Simes test. The paper of Simes may be considered as a basic step in the development of many new test procedures and new error rate criteria as for example control of the false discovery rate. A key issue is the validity of the Simes test and the underlying Simes inequality under dependence. Although it has been proved that the Simes inequality is valid under suitable assumptions on dependence structures, important cases are not covered yet. In this note we investigate p-values based on exchangeable test statistics in order to explore reasons for the validity or failure of the Simes inequality. We provide sufficient conditions for the asymptotic validity of the Simes inequality and its possible strictness. We also show by means of an easy-to-compute counterexample that exchangeability by itself is not sufficient for the validity of the Simes inequality.

Suggested Citation

  • H. Finner & M. Roters & K. Strassburger, 2017. "On the Simes test under dependence," Statistical Papers, Springer, vol. 58(3), pages 775-789, September.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0725-8
    DOI: 10.1007/s00362-015-0725-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-015-0725-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-015-0725-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 499-516, December.
    2. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    3. Gontscharuk, Veronika & Finner, Helmut, 2013. "Asymptotic FDR control under weak dependence: A counterexample," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1888-1893.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiong, Peihan & Hu, Taizhong, 2022. "On Samuel’s p-value model and the Simes test under dependence," Statistics & Probability Letters, Elsevier, vol. 187(C).
    2. Fengqing Zhang & Jiangtao Gou, 2021. "Refined critical boundary with enhanced statistical power for non-directional two-sided tests in group sequential designs with multiple endpoints," Statistical Papers, Springer, vol. 62(3), pages 1265-1290, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nowak, Piotr Bolesław, 2016. "The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 49-54.
    2. Chi, Chang Koo & Murto, Pauli & Valimaki, Juuso, 2017. "All-Pay Auctions with Affiliated Values," MPRA Paper 80799, University Library of Munich, Germany.
    3. Vikram Krishnamurthy & Udit Pareek, 2015. "Myopic Bounds for Optimal Policy of POMDPs: An Extension of Lovejoy’s Structural Results," Operations Research, INFORMS, vol. 63(2), pages 428-434, April.
    4. Badía, F.G. & Sangüesa, C. & Cha, J.H., 2014. "Stochastic comparison of multivariate conditionally dependent mixtures," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 82-94.
    5. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    6. Patricio S. Dalton & Sayantan Ghosal & Anandi Mani, 2016. "Poverty and Aspirations Failure," Economic Journal, Royal Economic Society, vol. 126(590), pages 165-188, February.
    7. Bhattacharya, Bhaskar, 2012. "Covariance selection and multivariate dependence," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 212-228.
    8. Castaño-Martínez, A. & Pigueiras, G. & Sordo, M.A., 2019. "On a family of risk measures based on largest claims," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 92-97.
    9. Elina Robeva & Bernd Sturmfels & Ngoc Tran & Caroline Uhler, 2021. "Maximum likelihood estimation for totally positive log‐concave densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 817-844, September.
    10. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2008. "Stein's phenomenon in estimation of means restricted to a polyhedral convex cone," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 141-164, January.
    11. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    12. Barmalzan, Ghobad & Akrami, Abbas & Balakrishnan, Narayanaswamy, 2020. "Stochastic comparisons of the smallest and largest claim amounts with location-scale claim severities," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 341-352.
    13. Lu, I-Li & Richards, Donald, 1996. "Total positivity properties of the bivariate diagonal natural exponential families," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 119-124, February.
    14. Junbo Son & Yeongin Kim & Shiyu Zhou, 2022. "Alerting patients via health information system considering trust-dependent patient adherence," Information Technology and Management, Springer, vol. 23(4), pages 245-269, December.
    15. Jian Yang, 2023. "A Partial Order for Strictly Positive Coalitional Games and a Link from Risk Aversion to Cooperation," Papers 2304.10652, arXiv.org.
    16. Michael Chwe, 2006. "Statistical Game Theory," Theory workshop papers 815595000000000004, UCLA Department of Economics.
    17. Chiaki Hara & Sujoy Mukerji & Frank Riedel & Jean-Marc Marc Tallon, 2022. "Efficient Allocations under Ambiguous Model Uncertainty," PSE Working Papers halshs-03828305, HAL.
    18. Battey, H.S. & Cox, D.R., 2022. "Some aspects of non-standard multivariate analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    19. Ligtvoet, R., 2015. "A test for using the sum score to obtain a stochastic ordering of subjects," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 136-139.
    20. Huang, Wen-Tao & Xu, Bing, 2002. "Some maximal inequalities and complete convergences of negatively associated random sequences," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 183-191, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0725-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.