IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v6y1976i4p473-499.html
   My bibliography  Save this article

Exponential inequalities for sums of random vectors

Author

Listed:
  • Yurinskii, V. V.

Abstract

This paper presents some generalizations of S. N. Bernstein's exponential bounds on probabilities of large deviations to the vector case. Inequalities for probabilities of large deviations of sums of independent random vectors are derived under a Cramér's type restriction on the rate of growth of absolute moments of the summands. Estimates are obtained for random vectors with values in Banach space, Sharper bounds hold in the case of finite-dimensional Euclidean or separable Hilbert spaces.

Suggested Citation

  • Yurinskii, V. V., 1976. "Exponential inequalities for sums of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 473-499, December.
    • Handle: RePEc:eee:jmvana:v:6:y:1976:i:4:p:473-499
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(76)90001-4
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Otsu, Taisuke, 2011. "Moderate deviations of generalized method of moments and empirical likelihood estimators," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1203-1216, September.
    2. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    3. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2006. "On the use of the bootstrap for estimating functions with functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1063-1074, November.
    4. Cattiaux, Patrick & Gozlan, Nathael, 2007. "Deviations bounds and conditional principles for thin sets," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 221-250, February.
    5. Cardot, Hervé & Sarda, Pacal, 2005. "Estimation in generalized linear models for functional data via penalized likelihood," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 24-41, January.
    6. Jan Mielniczuk & Małgorzata Wojtyś, 2010. "Estimation of Fisher information using model selection," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 163-187, September.
    7. Mason David M. & Eubank Randy, 2012. "Moderate deviations and intermediate efficiency for lack-of-fit tests," Statistics & Risk Modeling, De Gruyter, vol. 29(2), pages 175-187, June.
    8. Ferraty, F. & Van Keilegom, I. & Vieu, P., 2012. "Regression when both response and predictor are functions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 10-28.
    9. Dahmani, Abdelnasser & Ait Saidi, Ahmed & Bouhmila, Fatah & Aissani, Mouloud, 2009. "Consistency of the Tikhonov's regularization in an ill-posed problem with random data," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 722-727, March.
    10. Chen, Xia, 1997. "Moderate deviations for m-dependent random variables with Banach space values," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 123-134, September.
    11. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    12. Ahmedou, Aziza & Marion, Jean-Marie & Pumo, Besnik, 2016. "Generalized linear model with functional predictors and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 313-324.
    13. Inglot, Tadeusz, 2000. "On large deviation theorem for data-driven Neyman's statistic," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 411-419, May.
    14. Menneteau, Ludovic, 2005. "Some laws of the iterated logarithm in Hilbertian autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 405-425, February.

    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:jmvana:v:6:y:1976:i:4:p:473-499. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.