IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v65y2024i3d10.1007_s00362-023-01445-w.html
   My bibliography  Save this article

A unifying framework for rank and pseudo-rank based inference using nonparametric confidence distributions

Author

Listed:
  • Jonas Beck

    (Paris-Lodron-University of Salzburg)

  • Arne C. Bathke

    (Paris-Lodron-University of Salzburg)

Abstract

Nonparametric confidence distributions estimate statistical functionals by a distribution function on the parameter space, instead of the classical point or interval estimators. The concept bears analogy to the Bayesian posterior, but is nevertheless a completely frequentist concept. In order to ensure the desired statistical properties, we require that the cumulative distribution function on the parameter space is, evaluated at the true parameter, uniformly distributed over the unit interval. Our main focus lies on developing confidence distributions for the nonparametric relative effect and some natural extensions thereof. We develop asymptotic, range preserving and—especially important in the case of small sample sizes—approximate confidence distributions based on rank and pseudo-rank procedures. Due to the close relationship between point estimators, confidence intervals and p-values, these can all be approached in a unified manner within the framework of confidence distributions. The main goal of our contribution is to make the powerful theory of confidence distributions available in a nonparametric context, that is, for situations where methods relying on parametric assumptions are not justifiable. Application of the proposed methods and interpretation of the results is demonstrated using real data sets, including ordinal, non-metric data.

Suggested Citation

  • Jonas Beck & Arne C. Bathke, 2024. "A unifying framework for rank and pseudo-rank based inference using nonparametric confidence distributions," Statistical Papers, Springer, vol. 65(3), pages 1233-1257, May.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01445-w
    DOI: 10.1007/s00362-023-01445-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-023-01445-w
    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/s00362-023-01445-w?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. Dungang Liu & Regina Y. Liu & Min-ge Xie, 2014. "Exact Meta-Analysis Approach for Discrete Data and its Application to 2 × 2 Tables With Rare Events," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1450-1465, December.
    2. Jieli Shen & Regina Y. Liu & Min-ge Xie, 2020. "iFusion: Individualized Fusion Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1251-1267, July.
    3. Min-ge Xie & Kesar Singh, 2013. "Confidence Distribution, the Frequentist Distribution Estimator of a Parameter: A Review," International Statistical Review, International Statistical Institute, vol. 81(1), pages 3-39, April.
    4. Lu Tian & Rui Wang & Tianxi Cai & Lee-Jen Wei, 2011. "The Highest Confidence Density Region and Its Usage for Joint Inferences about Constrained Parameters," Biometrics, The International Biometric Society, vol. 67(2), pages 604-610, June.
    5. Edgar Brunner & Frank Konietschke & Arne C. Bathke & Markus Pauly, 2021. "Ranks and Pseudo‐ranks—Surprising Results of Certain Rank Tests in Unbalanced Designs," International Statistical Review, International Statistical Institute, vol. 89(2), pages 349-366, August.
    6. Dungang Liu & Regina Y. Liu & Minge Xie, 2015. "Multivariate Meta-Analysis of Heterogeneous Studies Using Only Summary Statistics: Efficiency and Robustness," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 326-340, March.
    7. Tore Schweder & Nils Lid Hjort, 2002. "Confidence and Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(2), pages 309-332, June.
    8. Edgar Brunner & Frank Konietschke & Markus Pauly & Madan L. Puri, 2017. "Rank-based procedures in factorial designs: hypotheses about non-parametric treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1463-1485, November.
    9. Xiaokang Luo & Tirthankar Dasgupta & Minge Xie & Regina Y. Liu, 2021. "Leveraging the Fisher randomization test using confidence distributions: Inference, combination and fusion learning," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 777-797, September.
    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. Liu, Xuhua & Li, Na & Hu, Yuqin, 2015. "Combining inferences on the common mean of several inverse Gaussian distributions based on confidence distribution," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 136-142.
    2. Guang Yang & Dungang Liu & Junyuan Wang & Min‐ge Xie, 2016. "Meta‐analysis framework for exact inferences with application to the analysis of rare events," Biometrics, The International Biometric Society, vol. 72(4), pages 1378-1386, December.
    3. David R. Bickel, 2014. "Small-scale Inference: Empirical Bayes and Confidence Methods for as Few as a Single Comparison," International Statistical Review, International Statistical Institute, vol. 82(3), pages 457-476, December.
    4. Wei Wang & Shou‐En Lu & Jerry Q. Cheng & Minge Xie & John B. Kostis, 2022. "Multivariate survival analysis in big data: A divide‐and‐combine approach," Biometrics, The International Biometric Society, vol. 78(3), pages 852-866, September.
    5. La Vecchia, Davide & Moor, Alban & Scaillet, Olivier, 2023. "A higher-order correct fast moving-average bootstrap for dependent data," Journal of Econometrics, Elsevier, vol. 235(1), pages 65-81.
    6. Zhao, Xiujie & Chen, Piao & Gaudoin, Olivier & Doyen, Laurent, 2021. "Accelerated degradation tests with inspection effects," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1099-1114.
    7. Veronese, Piero & Melilli, Eugenio, 2018. "Some asymptotic results for fiducial and confidence distributions," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 98-105.
    8. Nezakati, Ensiyeh & Pircalabelu, Eugen, 2021. "Unbalanced distributed estimation and inference for precision matrices," LIDAM Discussion Papers ISBA 2021031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Xuhua Liu & Xingzhong Xu, 2016. "Confidence distribution inferences in one-way random effects model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 59-74, March.
    10. Tang, Lu & Zhou, Ling & Song, Peter X.-K., 2020. "Distributed simultaneous inference in generalized linear models via confidence distribution," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    11. Piero Veronese & Eugenio Melilli, 2015. "Fiducial and Confidence Distributions for Real Exponential Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 471-484, June.
    12. David R. Bickel, 2024. "Bayesian and frequentist inference derived from the maximum entropy principle with applications to propagating uncertainty about statistical methods," Statistical Papers, Springer, vol. 65(8), pages 5389-5407, October.
    13. Xiaokang Luo & Tirthankar Dasgupta & Minge Xie & Regina Y. Liu, 2021. "Leveraging the Fisher randomization test using confidence distributions: Inference, combination and fusion learning," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 777-797, September.
    14. Piero Veronese & Eugenio Melilli, 2021. "Confidence Distribution for the Ability Parameter of the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 131-166, March.
    15. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    16. Yang Liu & Jan Hannig, 2017. "Generalized Fiducial Inference for Logistic Graded Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1097-1125, December.
    17. Nancy Reid & David R. Cox, 2015. "On Some Principles of Statistical Inference," International Statistical Review, International Statistical Institute, vol. 83(2), pages 293-308, August.
    18. Ruoyu Wang & Qihua Wang & Wang Miao, 2023. "A robust fusion-extraction procedure with summary statistics in the presence of biased sources," Biometrika, Biometrika Trust, vol. 110(4), pages 1023-1040.
    19. Eugenio Melilli & Piero Veronese, 2024. "Confidence distributions and hypothesis testing," Statistical Papers, Springer, vol. 65(6), pages 3789-3820, August.
    20. Fernando Delbianco & Fernando Tohmé, 2023. "Individualized Conformal," Working Papers 247, Red Nacional de Investigadores en Economía (RedNIE).

    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:65:y:2024:i:3:d:10.1007_s00362-023-01445-w. 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.