IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v107y2015icp236-245.html
   My bibliography  Save this article

On the weak laws of large numbers for sums of negatively associated random vectors in Hilbert spaces

Author

Listed:
  • Hien, N.T.T.
  • Thanh, L.V.

Abstract

This note establishes the weak law of large numbers for sums of negatively associated random vectors in Hilbert spaces. Illustrative examples are provided, one of which shows that the conditions for the weak law of large numbers cannot be dispensed with.

Suggested Citation

  • Hien, N.T.T. & Thanh, L.V., 2015. "On the weak laws of large numbers for sums of negatively associated random vectors in Hilbert spaces," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 236-245.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:236-245
    DOI: 10.1016/j.spl.2015.08.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771521500320X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.08.030?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. Chen, Xiaohong & White, Halbert, 1998. "Central Limit And Functional Central Limit Theorems For Hilbert-Valued Dependent Heterogeneous Arrays With Applications," Econometric Theory, Cambridge University Press, vol. 14(2), pages 260-284, April.
    2. Dehling, Herold & Sharipov, Olimjon Sh. & Wendler, Martin, 2015. "Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 200-215.
    3. Zhang, Li-Xin, 2001. "Strassen's law of the iterated logarithm for negatively associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 311-328, 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. Chang, Mengmeng & Miao, Yu, 2023. "Generalized weak laws of large numbers in Hilbert spaces," Statistics & Probability Letters, Elsevier, vol. 197(C).

    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. Bucchia, Béatrice & Wendler, Martin, 2017. "Change-point detection and bootstrap for Hilbert space valued random fields," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 344-368.
    2. Shao, Xiaofeng, 2011. "A bootstrap-assisted spectral test of white noise under unknown dependence," Journal of Econometrics, Elsevier, vol. 162(2), pages 213-224, June.
    3. R. Anton Braun & Huiyu Li & John Stachurski, 2012. "Generalized Look-Ahead Methods for Computing Stationary Densities," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 489-500, August.
    4. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2010. "Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 625-636, March.
    5. Chen Xiaohong & White Halbert, 2002. "Asymptotic Properties of Some Projection-based Robbins-Monro Procedures in a Hilbert Space," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(1), pages 1-55, April.
    6. Dong, Hao & Taylor, Luke, 2022. "Nonparametric Significance Testing In Measurement Error Models," Econometric Theory, Cambridge University Press, vol. 38(3), pages 454-496, June.
    7. Berkes, István & Horváth, Lajos & Rice, Gregory, 2016. "On the asymptotic normality of kernel estimators of the long run covariance of functional time series," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 150-175.
    8. Marine Carrasco & Barbara Rossi, 2016. "In-Sample Inference and Forecasting in Misspecified Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 313-338, July.
    9. Steffen Betsch & Bruno Ebner, 2019. "A new characterization of the Gamma distribution and associated goodness-of-fit tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 779-806, October.
    10. Florens, Jean-Pierre & Simoni, Anna, 2012. "Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior," Journal of Econometrics, Elsevier, vol. 170(2), pages 458-475.
    11. Won-Ki Seo, 2020. "Functional Principal Component Analysis for Cointegrated Functional Time Series," Papers 2011.12781, arXiv.org, revised Apr 2023.
    12. Dehling, Herold & Sharipov, Olimjon Sh. & Wendler, Martin, 2015. "Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 200-215.
    13. Kokoszka, Piotr & Reimherr, Matthew, 2013. "Asymptotic normality of the principal components of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1546-1562.
    14. Jiménez-Gamero, M.D. & Alba-Fernández, M.V., 2021. "A test for the geometric distribution based on linear regression of order statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 103-123.
    15. Chen, Xiaohong & Fan, Yanqin, 1999. "Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series," Journal of Econometrics, Elsevier, vol. 91(2), pages 373-401, August.
    16. Amengual, Dante & Carrasco, Marine & Sentana, Enrique, 2020. "Testing distributional assumptions using a continuum of moments," Journal of Econometrics, Elsevier, vol. 218(2), pages 655-689.
    17. Song, Kyungchul, 2010. "Testing semiparametric conditional moment restrictions using conditional martingale transforms," Journal of Econometrics, Elsevier, vol. 154(1), pages 74-84, January.
    18. Ta Cong Son & Le Van Dung, 2022. "Central Limit Theorems for Weighted Sums of Dependent Random Vectors in Hilbert Spaces via the Theory of the Regular Variation," Journal of Theoretical Probability, Springer, vol. 35(2), pages 988-1012, June.
    19. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Testing the martingale difference hypothesis using integrated regression functions," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2278-2294, December.
    20. Carrasco, Marine & Chernov, Mikhaël & Florens, Jean-Pierre & Ghysels, Eric, 2000. "Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions," IDEI Working Papers 116, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2002.

    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:107:y:2015:i:c:p:236-245. 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.