IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i2p427-437.html
   My bibliography  Save this article

A Bernstein-type estimator for decreasing density with application to p-value adjustments

Author

Listed:
  • Han, Bing
  • Dalal, Siddhartha R.

Abstract

The nonparametric maximum likelihood estimator (NPMLE) is a popular approach to estimating decreasing densities, i.e., f(s)≥f(t),s≤t. A less ideal feature of NPMLE is its step-function form. In this paper, we propose two nonparametric density estimators based on the Bernstein-type polynomials of the NPMLE. The proposed estimators have relatively simple forms and easy implementation. They have satisfactory smoothness as well as estimation efficiency. Numerical examples demonstrate the superior performance of the proposed estimators compared to existing methods. Decreasing densities have been applied in simultaneous inference to estimate the proportion of true null hypotheses and the local false discovery rate. We applied the proposed estimators to conduct simultaneous tests for a gene expression data set.

Suggested Citation

  • Han, Bing & Dalal, Siddhartha R., 2012. "A Bernstein-type estimator for decreasing density with application to p-value adjustments," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 427-437.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:2:p:427-437
    DOI: 10.1016/j.csda.2011.08.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003094
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2011.08.010?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. Kim‐Anh Do & Peter Müller & Feng Tang, 2005. "A Bayesian mixture model for differential gene expression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 627-644, June.
    2. 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.
    3. Sonia Petrone & Larry Wasserman, 2002. "Consistency of Bernstein polynomial posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 79-100, January.
    4. Efron, Bradley, 2004. "Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 96-104, January.
    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. 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.

    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. Mark A. van de Wiel & Kyung In Kim, 2007. "Estimating the False Discovery Rate Using Nonparametric Deconvolution," Biometrics, The International Biometric Society, vol. 63(3), pages 806-815, September.
    2. 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.
    3. Yu, Chang & Zelterman, Daniel, 2017. "A parametric model to estimate the proportion from true null using a distribution for p-values," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 105-118.
    4. Michele Guindani & Wesley O. Johnson, 2018. "More nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 239-251, June.
    5. 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.
    6. Hong, Zhaoping & Lian, Heng, 2012. "BOPA: A Bayesian hierarchical model for outlier expression detection," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4146-4156.
    7. 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.
    8. Bickel David R., 2008. "Correcting the Estimated Level of Differential Expression for Gene Selection Bias: Application to a Microarray Study," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-27, March.
    9. Montazeri Zahra & Yanofsky Corey M. & Bickel David R., 2010. "Shrinkage Estimation of Effect Sizes as an Alternative to Hypothesis Testing Followed by Estimation in High-Dimensional Biology: Applications to Differential Gene Expression," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-33, June.
    10. Marot Guillemette & Mayer Claus-Dieter, 2009. "Sequential Analysis for Microarray Data Based on Sensitivity and Meta-Analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-35, January.
    11. Rossell David & Guerra Rudy & Scott Clayton, 2008. "Semi-Parametric Differential Expression Analysis via Partial Mixture Estimation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-29, April.
    12. Chang Yu & Daniel Zelterman, 2020. "Distributions associated with simultaneous multiple hypothesis testing," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-17, December.
    13. Bradley Efron, 2007. "Doing thousands of hypothesis tests at the same time," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 3-21.
    14. Bing Han & Siddhartha R. Dalal & Daniel F. McCaffrey, 2012. "Simultaneous One-Sided Tests With Application to Education Evaluation Systems," Journal of Educational and Behavioral Statistics, , vol. 37(1), pages 114-136, February.
    15. Yao Luo & Peijun Sang & Ruli Xiao, 2024. "Order Statistics Approaches to Unobserved Heterogeneity in Auctions," Working Papers tecipa-776, University of Toronto, Department of Economics.
    16. Pounds Stanley B. & Gao Cuilan L. & Zhang Hui, 2012. "Empirical Bayesian Selection of Hypothesis Testing Procedures for Analysis of Sequence Count Expression Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(5), pages 1-32, October.
    17. van Wieringen, Wessel N. & Stam, Koen A. & Peeters, Carel F.W. & van de Wiel, Mark A., 2020. "Updating of the Gaussian graphical model through targeted penalized estimation," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    18. Ian W. McKeague & Min Qian, 2015. "An Adaptive Resampling Test for Detecting the Presence of Significant Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1422-1433, December.
    19. Yuhui Chen & Timothy Hanson & Jiajia Zhang, 2014. "Accelerated hazards model based on parametric families generalized with Bernstein polynomials," Biometrics, The International Biometric Society, vol. 70(1), pages 192-201, March.
    20. repec:jss:jstsof:40:i14 is not listed on IDEAS
    21. He, Yi & Pan, Wei & Lin, Jizhen, 2006. "Cluster analysis using multivariate normal mixture models to detect differential gene expression with microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 641-658, November.

    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:eee:csdana:v:56:y:2012:i:2:p:427-437. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.