IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2303.14088.html
   My bibliography  Save this paper

On the failure of the bootstrap for Chatterjee's rank correlation

Author

Listed:
  • Zhexiao Lin
  • Fang Han

Abstract

While researchers commonly use the bootstrap for statistical inference, many of us have realized that the standard bootstrap, in general, does not work for Chatterjee's rank correlation. In this paper, we provide proof of this issue under an additional independence assumption, and complement our theory with simulation evidence for general settings. Chatterjee's rank correlation thus falls into a category of statistics that are asymptotically normal but bootstrap inconsistent. Valid inferential methods in this case are Chatterjee's original proposal (for testing independence) and Lin and Han (2022)'s analytic asymptotic variance estimator (for more general purposes).

Suggested Citation

  • Zhexiao Lin & Fang Han, 2023. "On the failure of the bootstrap for Chatterjee's rank correlation," Papers 2303.14088, arXiv.org, revised Apr 2023.
    • Handle: RePEc:arx:papers:2303.14088
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2303.14088
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Qingyang, 2023. "On the asymptotic null distribution of the symmetrized Chatterjee’s correlation coefficient," Statistics & Probability Letters, Elsevier, vol. 194(C).
    2. Hall, Peter & Hardle, Wolfgang & Simar, Leopold, 1993. "On the inconsistency of bootstrap distribution estimators," Computational Statistics & Data Analysis, Elsevier, vol. 16(1), pages 11-18, June.
    3. Rudolf Beran, 1997. "Diagnosing Bootstrap Success," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 1-24, March.
    4. H Shi & M Drton & F Han, 2022. "On the power of Chatterjee’s rank correlation [Adaptive test of independence based on HSIC measures]," Biometrika, Biometrika Trust, vol. 109(2), pages 317-333.
    5. Mathias Drton & Benjamin Williams, 2011. "Quantifying the failure of bootstrap likelihood ratio tests," Biometrika, Biometrika Trust, vol. 98(4), pages 919-934.
    6. Alberto Abadie & Guido W. Imbens, 2008. "On the Failure of the Bootstrap for Matching Estimators," Econometrica, Econometric Society, vol. 76(6), pages 1537-1557, November.
    7. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
    8. Holger Dette & Karl F. Siburg & Pavel A. Stoimenov, 2013. "A Copula-Based Non-parametric Measure of Regression Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 21-41, March.
    9. Zheng Fang & Andres Santos, 2019. "Inference on Directionally Differentiable Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 377-412.
    10. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, July.
    11. Richard Samworth, 2003. "A note on methods of restoring consistency to the bootstrap," Biometrika, Biometrika Trust, vol. 90(4), pages 985-990, December.
    12. Sourav Chatterjee, 2021. "A New Coefficient of Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 2009-2022, October.
    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. Yihui He & Fang Han, 2023. "On propensity score matching with a diverging number of matches," Papers 2310.14142, arXiv.org, revised Nov 2023.

    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. Kitagawa, Toru & Montiel Olea, José Luis & Payne, Jonathan & Velez, Amilcar, 2020. "Posterior distribution of nondifferentiable functions," Journal of Econometrics, Elsevier, vol. 217(1), pages 161-175.
    2. Zhang, Qingyang, 2023. "On the asymptotic null distribution of the symmetrized Chatterjee’s correlation coefficient," Statistics & Probability Letters, Elsevier, vol. 194(C).
    3. Donald W.K. Andrews & Sukjin Han, 2008. "Invalidity of the Bootstrap and the m Out of n Bootstrap for Interval Endpoints Defined by Moment Inequalities," Cowles Foundation Discussion Papers 1671, Cowles Foundation for Research in Economics, Yale University.
    4. Qingyang Zhang, 2024. "Asymptotic expected sensitivity function and its applications to measures of monotone association," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 877-896, October.
    5. Chunlin Wang & Paul Marriott & Pengfei Li, 2022. "A note on the coverage behaviour of bootstrap percentile confidence intervals for constrained parameters," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(7), pages 809-831, October.
    6. 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.
    7. Yihui He & Fang Han, 2023. "On propensity score matching with a diverging number of matches," Papers 2310.14142, arXiv.org, revised Nov 2023.
    8. Fang Han, 2024. "An Introduction to Permutation Processes (version 0.5)," Papers 2407.09664, arXiv.org.
    9. Wang, Weizhen, 2013. "A note on bootstrap confidence intervals for proportions," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2699-2702.
    10. Cavaliere, Giuseppe & Nielsen, Heino Bohn & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2022. "Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models," Journal of Econometrics, Elsevier, vol. 227(1), pages 241-263.
    11. Ghosal, Rahul & Ghosh, Sujit K., 2022. "Bayesian inference for generalized linear model with linear inequality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    12. Joel L. Horowitz, 2018. "Bootstrap Methods in Econometrics," Papers 1809.04016, arXiv.org.
    13. Sun, Zhenting, 2023. "Instrument validity for heterogeneous causal effects," Journal of Econometrics, Elsevier, vol. 237(2).
    14. Giurcanu, Mihai C., 2012. "Bootstrapping in non-regular smooth function models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 78-93.
    15. Joel L. Horowitz, 2018. "Bootstrap methods in econometrics," CeMMAP working papers CWP53/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Giuseppe Cavaliere & Iliyan Georgiev, 2020. "Inference Under Random Limit Bootstrap Measures," Econometrica, Econometric Society, vol. 88(6), pages 2547-2574, November.
    17. Hongyi Jiang & Zhenting Sun & Shiyun Hu, 2023. "A Nonparametric Test of $m$th-degree Inverse Stochastic Dominance," Papers 2306.12271, arXiv.org, revised Jul 2023.
    18. H Shi & M Drton & F Han, 2022. "On the power of Chatterjee’s rank correlation [Adaptive test of independence based on HSIC measures]," Biometrika, Biometrika Trust, vol. 109(2), pages 317-333.
    19. Junlong Feng & Sokbae Lee, 2023. "Individual Welfare Analysis: Random Quasilinear Utility, Independence, and Confidence Bounds," Papers 2304.01921, arXiv.org, revised Jun 2024.
    20. van de Walle, Dominique & Mu, Ren, 2007. "Fungibility and the flypaper effect of project aid: Micro-evidence for Vietnam," Journal of Development Economics, Elsevier, vol. 84(2), pages 667-685, November.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2303.14088. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.