IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v73y2005i2p189-197.html
   My bibliography  Save this article

An exponential inequality for associated variables

Author

Listed:
  • Oliveira, Paulo Eduardo

Abstract

We prove an exponential inequality for positively associated and strictly stationary random variables replacing an uniform boundedness assumption by the existence of Laplace transforms. The proof uses a truncation technique together with a block decomposition of the sums to allow an approximation to independence. We show that for geometrically decreasing covariances our conditions are fulfilled, identifying a convergence rate for the strong law of large numbers.

Suggested Citation

  • Oliveira, Paulo Eduardo, 2005. "An exponential inequality for associated variables," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 189-197, June.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:2:p:189-197
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00033-7
    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. Lesigne, Emmanuel & Volný, Dalibor, 2001. "Large deviations for martingales," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 143-159, November.
    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. Sung, Soo Hak, 2007. "A note on the exponential inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1730-1736, December.
    2. Yang, Shanchao & Su, Chun & Yu, Keming, 2008. "A general method to the strong law of large numbers and its applications," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 794-803, April.
    3. Guodong Xing & Shanchao Yang, 2010. "Some Exponential Inequalities for Positively Associated Random Variables and Rates of Convergence of the Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 23(1), pages 169-192, March.

    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. Fan, Xiequan & Alquier, Pierre & Doukhan, Paul, 2022. "Deviation inequalities for stochastic approximation by averaging," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 452-485.
    2. Zhou, Xing-cai & Lin, Jin-guan, 2012. "A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error’s structure," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1914-1922.
    3. Giraudo, Davide, 2016. "Holderian weak invariance principle under a Hannan type condition," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 290-311.
    4. Boucher, Thomas R., 2016. "A note on martingale deviation bounds," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 8-11.
    5. Chen, Qisheng & Zhang, Qian & Liu, Chuan, 2019. "The pricing and numerical analysis of lookback options for mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 123-128.
    6. Emmanuel Rio, 2009. "Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 146-163, March.
    7. Kanaya, Shin & Otsu, Taisuke, 2012. "Large deviations of realized volatility," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 546-581.
    8. Dedecker, Jérôme & Fan, Xiequan, 2015. "Deviation inequalities for separately Lipschitz functionals of iterated random functions," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 60-90.
    9. Anders Bredahl Kock, 2013. "Oracle inequalities for high-dimensional panel data models," CREATES Research Papers 2013-20, Department of Economics and Business Economics, Aarhus University.
    10. Hua-Ming Wang, 2018. "Law of Large Numbers for Random Walk with Unbounded Jumps and Birth and Death Process with Bounded Jumps in Random Environment," Journal of Theoretical Probability, Springer, vol. 31(2), pages 619-642, June.
    11. Stoica, George, 2008. "The Baum-Katz theorem for bounded subsequences," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 924-926, May.
    12. Fan, Xiequan & Grama, Ion & Liu, Quansheng, 2012. "Hoeffding’s inequality for supermartingales," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3545-3559.
    13. Li, Yulin, 2003. "A martingale inequality and large deviations," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 317-321, April.
    14. H. Nooghabi & H. Azarnoosh, 2009. "Exponential inequality for negatively associated random variables," Statistical Papers, Springer, vol. 50(2), pages 419-428, March.
    15. Liu, Quansheng & Watbled, Frédérique, 2009. "Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3101-3132, October.
    16. Anders Bredahl Kock & Haihan Tang, 2014. "Inference in High-dimensional Dynamic Panel Data Models," CREATES Research Papers 2014-58, Department of Economics and Business Economics, Aarhus University.
    17. Lacoin, Hubert & Moreno, Gregorio, 2010. "Directed polymers on hierarchical lattices with site disorder," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 467-493, April.

    More about this item

    Keywords

    Association Exponential inequality;

    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:eee:stapro:v:73:y:2005:i:2:p:189-197. 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.