IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v50y2023i4p1616-1640.html
   My bibliography  Save this article

Finite sample inference for empirical Bayesian methods

Author

Listed:
  • Hien Duy Nguyen
  • Mayetri Gupta

Abstract

In recent years, empirical Bayesian (EB) inference has become an attractive approach for estimation in parametric models arising in a variety of real‐life problems, especially in complex and high‐dimensional scientific applications. However, compared to the relative abundance of available general methods for computing point estimators in the EB framework, the construction of confidence sets and hypothesis tests with good theoretical properties remains difficult and problem specific. Motivated by the Universal Inference framework, we propose a general and universal method, based on holdout likelihood ratios, and utilizing the hierarchical structure of the specified Bayesian model for constructing confidence sets and hypothesis tests that are finite sample valid. We illustrate our method through a range of numerical studies and real data applications, which demonstrate that the approach is able to generate useful and meaningful inferential statements in the relevant contexts.

Suggested Citation

  • Hien Duy Nguyen & Mayetri Gupta, 2023. "Finite sample inference for empirical Bayesian methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(4), pages 1616-1640, December.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:4:p:1616-1640
    DOI: 10.1111/sjos.12643
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12643
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12643?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
    ---><---

    References listed on IDEAS

    as
    1. Svend Haastrup, 2000. "Comparison of Some Bayesian Analyses of Heterogeneity in Group Life Insurance," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2000(1), pages 2-16.
    2. J. T. Gene Hwang & Zhigen Zhao, 2013. "Empirical Bayes Confidence Intervals for Selected Parameters in High-Dimensional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 607-618, June.
    3. Glenn Shafer, 2021. "Testing by betting: A strategy for statistical and scientific communication," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(2), pages 407-431, April.
    4. Jiaying Gu & Roger Koenker, 2017. "Rebayes: an R package for empirical bayes mixture methods," CeMMAP working papers 37/17, Institute for Fiscal Studies.
    5. J. T. Gene Hwang & Jing Qiu & Zhigen Zhao, 2009. "Empirical Bayes confidence intervals shrinking both means and variances," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 265-285, January.
    6. Gauri Sankar Datta & Malay Ghosh & David Daniel Smith & Parthasarathi Lahiri, 2002. "On an Asymptotic Theory of Conditional and Unconditional Coverage Probabilities of Empirical Bayes Confidence Intervals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 139-152, March.
    7. Johnstone, Iain & Silverman, Bernard W., 2005. "EbayesThresh: R Programs for Empirical Bayes Thresholding," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i08).
    Full references (including those not matched with items on IDEAS)

    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. Yeil Kwon & Zhigen Zhao, 2023. "On F-modelling-based empirical Bayes estimation of variances," Biometrika, Biometrika Trust, vol. 110(1), pages 69-81.
    2. Kubokawa, Tatsuya & Nagashima, Bui, 2012. "Parametric bootstrap methods for bias correction in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 1-16.
    3. Bing-Yi Jing & Zhouping Li & Guangming Pan & Wang Zhou, 2016. "On SURE-Type Double Shrinkage Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1696-1704, October.
    4. Lixia Diao & David D. Smith & Gauri Sankar Datta & Tapabrata Maiti & Jean D. Opsomer, 2014. "Accurate Confidence Interval Estimation of Small Area Parameters Under the Fay–Herriot Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 497-515, June.
    5. Turner, Rosanne J. & Grünwald, Peter D., 2023. "Exact anytime-valid confidence intervals for contingency tables and beyond," Statistics & Probability Letters, Elsevier, vol. 198(C).
    6. Malay Ghosh & Tapabrata Maiti, 2008. "Empirical Bayes Confidence Intervals for Means of Natural Exponential Family‐Quadratic Variance Function Distributions with Application to Small Area Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 484-495, September.
    7. Hajime Uno & Lu Tian & L.J. Wei, 2004. "The Optimal Confidence Region for a Random Parameter," Harvard University Biostatistics Working Paper Series 1013, Berkeley Electronic Press.
    8. Zhigen Zhao, 2022. "Where to find needles in a haystack?," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 148-174, March.
    9. Ruodu Wang & Aaditya Ramdas, 2022. "False discovery rate control with e‐values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 822-852, July.
    10. Maarten Jansen & Guy P. Nason & B. W. Silverman, 2009. "Multiscale methods for data on graphs and irregular multidimensional situations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 97-125, January.
    11. Tatsuya Kubokawa, 2010. "On Measuring Uncertainty of Small Area Estimators with Higher Order Accuracy," CIRJE F-Series CIRJE-F-754, CIRJE, Faculty of Economics, University of Tokyo.
    12. Thomas Cook & Patrick Flaherty, 2024. "Hedging in Sequential Experiments," Papers 2406.15867, arXiv.org.
    13. Peter A. Gao & Jonathan Wakefield, 2023. "A Spatial Variance‐Smoothing Area Level Model for Small Area Estimation of Demographic Rates," International Statistical Review, International Statistical Institute, vol. 91(3), pages 493-510, December.
    14. Hirose, Masayo Yoshimori, 2017. "Non-area-specific adjustment factor for second-order efficient empirical Bayes confidence interval," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 67-78.
    15. Berg Emily, 2022. "Construction of Databases for Small Area Estimation," Journal of Official Statistics, Sciendo, vol. 38(3), pages 673-708, September.
    16. Alexander Henzi & Johanna F Ziegel, 2022. "Valid sequential inference on probability forecast performance [A comparison of the ECMWF, MSC, and NCEP global ensemble prediction systems]," Biometrika, Biometrika Trust, vol. 109(3), pages 647-663.
    17. Sander Greenland, 2023. "Divergence versus decision P‐values: A distinction worth making in theory and keeping in practice: Or, how divergence P‐values measure evidence even when decision P‐values do not," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 54-88, March.
    18. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
    19. Park, Junyong, 2014. "Shrinkage estimator in normal mean vector estimation based on conditional maximum likelihood estimators," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 1-6.
    20. Pan, Jia-Chiun & Huang, Yufen & Hwang, J.T. Gene, 2017. "Estimation of selected parameters," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 45-63.

    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:50:y:2023:i:4:p:1616-1640. 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.