IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v182y2022ics0167715221002571.html
   My bibliography  Save this article

Gaussian approximations for high-dimensional non-degenerate U-statistics via exchangeable pairs

Author

Listed:
  • Cheng, Guanghui
  • Liu, Zhi
  • Peng, Liuhua

Abstract

In this paper, we obtain a non-asymptotic bound for Gaussian approximations for centered high-dimensional non-degenerate U-statistics over the class of hyperrectangles via exchangeable pairs and Stein’s method. We improve the upper bound of the convergence rate from n−1/6 in Chen (2018) to n−1/4 up to a polynomial factor of logd under the same conditions, where n is the sample size and d is the dimension of the U-statistic. Convergence to zero of the bound requires logd=o(n1/7) in Chen (2018), this requirement on d is weaken in this paper by allowing logd=o(n1/5).

Suggested Citation

  • Cheng, Guanghui & Liu, Zhi & Peng, Liuhua, 2022. "Gaussian approximations for high-dimensional non-degenerate U-statistics via exchangeable pairs," Statistics & Probability Letters, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:stapro:v:182:y:2022:i:c:s0167715221002571
    DOI: 10.1016/j.spl.2021.109295
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715221002571
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109295?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. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Yuta Koike, 2019. "Improved Central Limit Theorem and bootstrap approximations in high dimensions," Papers 1912.10529, arXiv.org, revised May 2022.
    2. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    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. Magne Mogstad & Joseph P Romano & Azeem M Shaikh & Daniel Wilhelm, 2024. "Inference for Ranks with Applications to Mobility across Neighbourhoods and Academic Achievement across Countries," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(1), pages 476-518.
    2. Chang, Jinyuan & Jiang, Qing & Shao, Xiaofeng, 2023. "Testing the martingale difference hypothesis in high dimension," Journal of Econometrics, Elsevier, vol. 235(2), pages 972-1000.
    3. David M. Ritzwoller & Vasilis Syrgkanis, 2024. "Simultaneous Inference for Local Structural Parameters with Random Forests," Papers 2405.07860, arXiv.org, revised Sep 2024.
    4. Kock, Anders Bredahl & Preinerstorfer, David, 2024. "A remark on moment-dependent phase transitions in high-dimensional Gaussian approximations," Statistics & Probability Letters, Elsevier, vol. 211(C).
    5. Matias D. Cattaneo & Ricardo P. Masini & William G. Underwood, 2022. "Yurinskii's Coupling for Martingales," Papers 2210.00362, arXiv.org, revised Sep 2024.
    6. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Yuta Koike, 2022. "High-dimensional Data Bootstrap," Papers 2205.09691, arXiv.org.
    7. Kojevnikov, Denis & Song, Kyungchul, 2022. "A Berry–Esseen bound for vector-valued martingales," Statistics & Probability Letters, Elsevier, vol. 186(C).
    8. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing Many Moment Inequalities," CeMMAP working papers 65/13, Institute for Fiscal Studies.
    9. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. repec:hum:wpaper:sfb649dp2015-031 is not listed on IDEAS
    11. repec:hum:wpaper:sfb649dp2014-067 is not listed on IDEAS
    12. Bakalli, Gaetan & Guerrier, Stéphane & Scaillet, Olivier, 2023. "A penalized two-pass regression to predict stock returns with time-varying risk premia," Journal of Econometrics, Elsevier, vol. 237(2).
    13. Shengchun Kong & Zhuqing Yu & Xianyang Zhang & Guang Cheng, 2021. "High‐dimensional robust inference for Cox regression models using desparsified Lasso," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 1068-1095, September.
    14. Brice Ozenne & Esben Budtz-Jørgensen & Sebastian Elgaard Ebert, 2023. "Controlling the familywise error rate when performing multiple comparisons in a linear latent variable model," Computational Statistics, Springer, vol. 38(1), pages 1-23, March.
    15. Jad Beyhum & Jonas Striaukas, 2023. "Testing for sparse idiosyncratic components in factor-augmented regression models," Papers 2307.13364, arXiv.org, revised Jul 2024.
    16. Hansen, Christian & Liao, Yuan, 2019. "The Factor-Lasso And K-Step Bootstrap Approach For Inference In High-Dimensional Economic Applications," Econometric Theory, Cambridge University Press, vol. 35(3), pages 465-509, June.
    17. Byol Kim & Song Liu & Mladen Kolar, 2021. "Two‐sample inference for high‐dimensional Markov networks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 939-962, November.
    18. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Uniform Post Selection Inference for LAD Regression and Other Z-estimation problems," Papers 1304.0282, arXiv.org, revised Oct 2020.
    19. Alexandre Belloni & Victor Chernozhukov & Abhishek Kaul, 2017. "Confidence bands for coefficients in high dimensional linear models with error-in-variables," CeMMAP working papers CWP22/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Matias D. Cattaneo & Richard K. Crump & Weining Wang, 2022. "Beta-Sorted Portfolios," Papers 2208.10974, arXiv.org, revised Nov 2024.
    21. Yuta Koike, 2023. "High-Dimensional Central Limit Theorems for Homogeneous Sums," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-45, March.
    22. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney K. Newey, 2016. "Double machine learning for treatment and causal parameters," CeMMAP working papers 49/16, Institute for Fiscal Studies.

    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:stapro:v:182:y:2022:i:c:s0167715221002571. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.