IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v74y1998i2p273-296.html
   My bibliography  Save this article

Moderate and large deviations for U-processes

Author

Listed:
  • Eichelsbacher, Peter

Abstract

Sufficient conditions for the moderate and large deviation principle for U-processes are given. For the large deviation result the conditions are in terms of "blockwise" empirical process conditions. On the moderate scaling the case of U-processes indexed by a uniformly bounded VC subgraph class of functions is considered. The proofs are based on an isoperimetric inequality for empirical processes due to Talagrand, a truncation method based on an isoperimetric inequality by Ledoux, the existence of almost regular partitions of complete hypergraphs due to Baranyai and a Bernstein-type inequality for U-processes due to Arcones and Giné.

Suggested Citation

  • Eichelsbacher, Peter, 1998. "Moderate and large deviations for U-processes," Stochastic Processes and their Applications, Elsevier, vol. 74(2), pages 273-296, June.
    • Handle: RePEc:eee:spapps:v:74:y:1998:i:2:p:273-296
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00113-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Arcones, Miguel A., 1995. "A Bernstein-type inequality for U-statistics and U-processes," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 239-247, February.
    2. Arcones, M. A., 1993. "The Law of the Iterated Logarithm for U-Processes," Journal of Multivariate Analysis, Elsevier, vol. 47(1), pages 139-151, October.
    3. Arcones, Miguel A. & Giné, Evarist, 1994. "U-processes indexed by Vapnik-Cervonenkis classes of functions with applications to asymptotics and bootstrap of U-statistics with estimated parameters," Stochastic Processes and their Applications, Elsevier, vol. 52(1), pages 17-38, August.
    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. Eichelsbacher, Peter, 2000. "Moderate deviations for degenerate U-processes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 255-279, June.

    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. Arcones, Miguel A. & Giné, Evarist, 1995. "On the law of the iterated logarithm for canonical U-statistics and processes," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 217-245, August.
    2. Pedro Delicado & Juan Romo, 1998. "Constant coefficient tests for random coefficient regression," Economics Working Papers 329, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Jianhang Ai & Ondřej Kuželka & Yuyi Wang, 2023. "Hoeffding–Serfling Inequality for U-Statistics Without Replacement," Journal of Theoretical Probability, Springer, vol. 36(1), pages 390-408, March.
    4. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2013. "Global Bahadur Representation For Nonparametric Censored Regression Quantiles And Its Applications," Econometric Theory, Cambridge University Press, vol. 29(5), pages 941-968, October.
    5. Yoshihiko Nishiyama & Peter M. Robinson, 2005. "The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 73(3), pages 903-948, May.
    6. Chen, Songnian, 2018. "Sequential estimation of censored quantile regression models," Journal of Econometrics, Elsevier, vol. 207(1), pages 30-52.
    7. Wendler, Martin, 2012. "U-processes, U-quantile processes and generalized linear statistics of dependent data," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 787-807.
    8. Miruna Oprescu & Vasilis Syrgkanis & Zhiwei Steven Wu, 2018. "Orthogonal Random Forest for Causal Inference," Papers 1806.03467, arXiv.org, revised Sep 2019.
    9. Eichelsbacher, Peter, 2000. "Moderate deviations for degenerate U-processes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 255-279, June.
    10. Subbotin, Viktor, 2007. "Asymptotic and bootstrap properties of rank regressions," MPRA Paper 9030, University Library of Munich, Germany, revised 20 Mar 2008.
    11. Salim Bouzebda & Amel Nezzal & Tarek Zari, 2022. "Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences," Mathematics, MDPI, vol. 11(1), pages 1-39, December.
    12. Kaoukeb Turki-Moalla, 1998. "Rates of Convergence and Law of the Iterated Logarithm for U-Processes," Journal of Theoretical Probability, Springer, vol. 11(4), pages 869-906, October.
    13. Cizek, Pavel & Sadikoglu, Serhan, 2022. "Nonseparable Panel Models with Index Structure and Correlated Random Effects," Other publications TiSEM 7899deb9-0eda-47e6-a3b8-2, Tilburg University, School of Economics and Management.
    14. Chen, Songnian & Wang, Qian, 2023. "Quantile regression with censoring and sample selection," Journal of Econometrics, Elsevier, vol. 234(1), pages 205-226.
    15. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    16. Subbotin, Viktor, 2008. "Essays on the econometric theory of rank regressions," MPRA Paper 14086, University Library of Munich, Germany.
    17. Krebs, Johannes T.N., 2018. "A large deviation inequality for β-mixing time series and its applications to the functional kernel regression model," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 50-58.

    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:spapps:v:74:y:1998:i:2:p:273-296. 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/505572/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.