IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v41y2014i4p1167-1194.html
   My bibliography  Save this article

On Efficient Estimators of the Proportion of True Null Hypotheses in a Multiple Testing Setup

Author

Listed:
  • Van Hanh Nguyen
  • Catherine Matias

Abstract

type="main" xml:id="sjos12091-abs-0001"> We consider the problem of estimating the proportion θ of true null hypotheses in a multiple testing context. The setup is classically modelled through a semiparametric mixture with two components: a uniform distribution on interval [0,1] with prior probability θ and a non-parametric density f . We discuss asymptotic efficiency results and establish that two different cases occur whether f vanishes on a non-empty interval or not. In the first case, we exhibit estimators converging at a parametric rate, compute the optimal asymptotic variance and conjecture that no estimator is asymptotically efficient (i.e. attains the optimal asymptotic variance). In the second case, we prove that the quadratic risk of any estimator does not converge at a parametric rate. We illustrate those results on simulated data.

Suggested Citation

  • Van Hanh Nguyen & Catherine Matias, 2014. "On Efficient Estimators of the Proportion of True Null Hypotheses in a Multiple Testing Setup," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1167-1194, December.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:4:p:1167-1194
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/sjos.12091
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, vol. 32(2), pages 189-218, July.
    2. Celisse, Alain & Robin, Stephane, 2008. "Nonparametric density estimation by exact leave-p-out cross-validation," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2350-2368, January.
    3. Mette Langaas & Bo Henry Lindqvist & Egil Ferkingstad, 2005. "Estimating the proportion of true null hypotheses, with application to DNA microarray data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 555-572, September.
    4. Nicolai Meinshausen & Peter Buhlmann, 2005. "Lower bounds for the number of false null hypotheses for multiple testing of associations under general dependence structures," Biometrika, Biometrika Trust, vol. 92(4), pages 893-907, December.
    5. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498, August.
    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. Jiali Zheng & Xiyang Wang, 2022. "Estimation for a Class of Semiparametric Pareto Mixture Densities," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 609-627, August.
    2. Rohit Kumar Patra & Bodhisattva Sen, 2016. "Estimation of a two-component mixture model with applications to multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 869-893, September.

    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. Rohit Kumar Patra & Bodhisattva Sen, 2016. "Estimation of a two-component mixture model with applications to multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 869-893, September.
    2. Helmut Finner & Veronika Gontscharuk, 2009. "Controlling the familywise error rate with plug‐in estimator for the proportion of true null hypotheses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1031-1048, November.
    3. Shigeyuki Matsui & Hisashi Noma, 2011. "Estimating Effect Sizes of Differentially Expressed Genes for Power and Sample-Size Assessments in Microarray Experiments," Biometrics, The International Biometric Society, vol. 67(4), pages 1225-1235, December.
    4. Timothy B. Armstrong, 2014. "Adaptive Testing on a Regression Function at a Point," Cowles Foundation Discussion Papers 1957R, Cowles Foundation for Research in Economics, Yale University, revised Feb 2015.
    5. Axel Gandy & Georg Hahn, 2016. "A Framework for Monte Carlo based Multiple Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1046-1063, December.
    6. Chen, Xiongzhi, 2019. "Uniformly consistently estimating the proportion of false null hypotheses via Lebesgue–Stieltjes integral equations," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 724-744.
    7. Zehetmayer Sonja & Graf Alexandra C. & Posch Martin, 2015. "Sample size reassessment for a two-stage design controlling the false discovery rate," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(5), pages 429-442, November.
    8. Davide Risso & Liam Purvis & Russell B Fletcher & Diya Das & John Ngai & Sandrine Dudoit & Elizabeth Purdom, 2018. "clusterExperiment and RSEC: A Bioconductor package and framework for clustering of single-cell and other large gene expression datasets," PLOS Computational Biology, Public Library of Science, vol. 14(9), pages 1-16, September.
    9. Friguet, Chloé & Causeur, David, 2011. "Estimation of the proportion of true null hypotheses in high-dimensional data under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2665-2676, September.
    10. T. Tony Cai & Wenguang Sun & Weinan Wang, 2019. "Covariate‐assisted ranking and screening for large‐scale two‐sample inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 187-234, April.
    11. David Ruppert & Dan Nettleton & J. T. Gene Hwang, 2007. "Exploring the Information in p-Values for the Analysis and Planning of Multiple-Test Experiments," Biometrics, The International Biometric Society, vol. 63(2), pages 483-495, June.
    12. Farcomeni, Alessio & Pacillo, Simona, 2011. "A conservative estimator for the proportion of false nulls based on Dvoretzky, Kiefer and Wolfowitz inequality," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1867-1870.
    13. Tim Bancroft & Chuanlong Du & Dan Nettleton, 2013. "Estimation of False Discovery Rate Using Sequential Permutation p-Values," Biometrics, The International Biometric Society, vol. 69(1), pages 1-7, March.
    14. Ferreira, J.A. & Nyangoma, S.O., 2008. "A multivariate version of the Benjamini-Hochberg method," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2108-2124, October.
    15. Campbell, Randall C. & Nagel, Gregory L., 2016. "Private information and limitations of Heckman's estimator in banking and corporate finance research," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 186-195.
    16. Youngchao Ge & Sandrine Dudoit & Terence Speed, 2003. "Resampling-based multiple testing for microarray data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 1-77, June.
    17. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
    18. Lanot, Gauthier & Walker, Ian, 1998. "The union/non-union wage differential: An application of semi-parametric methods," Journal of Econometrics, Elsevier, vol. 84(2), pages 327-349, June.
    19. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    20. Bajgrowicz, Pierre & Scaillet, Olivier, 2012. "Technical trading revisited: False discoveries, persistence tests, and transaction costs," Journal of Financial Economics, Elsevier, vol. 106(3), pages 473-491.

    More about this item

    Statistics

    Access and download statistics

    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:bla:scjsta:v:41:y:2014:i:4:p:1167-1194. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.