IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v117y2007i7p878-903.html
   My bibliography  Save this article

Probability and moment inequalities for sums of weakly dependent random variables, with applications

Author

Listed:
  • Doukhan, Paul
  • Neumann, Michael H.

Abstract

Doukhan and Louhichi [P. Doukhan, S. Louhichi, A new weak dependence condition and application to moment inequalities, Stochastic Process. Appl. 84 (1999) 313-342] introduced a new concept of weak dependence which is more general than mixing. Such conditions are particularly well suited for deriving estimates for the cumulants of sums of random variables. We employ such cumulant estimates to derive inequalities of Bernstein and Rosenthal type which both improve on previous results. Furthermore, we consider several classes of processes and show that they fulfill appropriate weak dependence conditions. We also sketch applications of our inequalities in probability and statistics.

Suggested Citation

  • Doukhan, Paul & Neumann, Michael H., 2007. "Probability and moment inequalities for sums of weakly dependent random variables, with applications," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 878-903, July.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:7:p:878-903
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(06)00160-8
    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. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    2. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
    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. Matteo Barigozzi & Christian Brownlees, 2019. "NETS: Network estimation for time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 347-364, April.
    2. Nassira Menni & Abdelkader Tatachak, 2018. "A note on estimating the conditional expectation under censoring and association: strong uniform consistency," Statistical Papers, Springer, vol. 59(3), pages 1009-1030, September.
    3. Matteo Barigozzi & Matteo Luciani, 2019. "Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm," Papers 1910.03821, arXiv.org, revised Sep 2024.
    4. Fan, Jianqing & Han, Fang & Liu, Han & Vickers, Byron, 2016. "Robust inference of risks of large portfolios," Journal of Econometrics, Elsevier, vol. 194(2), pages 298-308.
    5. Hafouta, Yeor, 2023. "Convergence rates in the functional CLT for α-mixing triangular arrays," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 242-290.
    6. Strauch, Claudia, 2015. "Sharp adaptive drift estimation for ergodic diffusions: The multivariate case," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2562-2602.
    7. Hwang, Eunju & Shin, Dong Wan, 2012. "Strong consistency of the stationary bootstrap under ψ-weak dependence," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 488-495.
    8. Eunju Hwang & Dong Shin, 2016. "Kernel estimators of mode under $$\psi $$ ψ -weak dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 301-327, April.
    9. Jianqing Fan & Jingjin Zhang & Ke Yu, 2008. "Asset Allocation and Risk Assessment with Gross Exposure Constraints for Vast Portfolios," Papers 0812.2604, arXiv.org.
    10. Alquier Pierre & Doukhan Paul & Fan Xiequan, 2019. "Exponential inequalities for nonstationary Markov chains," Dependence Modeling, De Gruyter, vol. 7(1), pages 150-168, January.
    11. Mikkelsen, Jakob Guldbæk & Hillebrand, Eric & Urga, Giovanni, 2019. "Consistent estimation of time-varying loadings in high-dimensional factor models," Journal of Econometrics, Elsevier, vol. 208(2), pages 535-562.
    12. Zohra Guessoum & Abdelkader Tatachak, 2020. "Asymptotic Results for Truncated-censored and Associated Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 142-164, May.
    13. Hwang, Eunju & Shin, Dong Wan, 2012. "Stationary bootstrap for kernel density estimators under ψ-weak dependence," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1581-1593.

    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. Doukhan, P. & Pommeret, D. & Reboul, L., 2015. "Data driven smooth test of comparison for dependent sequences," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 147-165.
    2. Paul Doukhan & Gilles Teyssière & Pablo Winant, 2005. "A Larch Vector Valued Process," Working Papers 2005-49, Center for Research in Economics and Statistics.
    3. Paul Doukhan & Olivier Wintenberger, 2005. "An Invariance Principle for New Weakly Dependent Stationary Models using Sharp Moment Assumptions," Working Papers 2005-51, Center for Research in Economics and Statistics.
    4. Doukhan, Paul & Fokianos, Konstantinos & Li, Xiaoyin, 2012. "On weak dependence conditions: The case of discrete valued processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1941-1948.
    5. Jean-Marc Bardet & Paul Doukhan & José Rafael Leon_, 2005. "Uniform Limit Theorems for the Integrated Periodogram of Weakly Dependent Time Series and their Applications to Whittle's Estimate," Working Papers 2005-46, Center for Research in Economics and Statistics.
    6. Rootzén, Holger, 2009. "Weak convergence of the tail empirical process for dependent sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 468-490, February.
    7. Paul Doukhan & Hélène Madre & Mathieu Rosenbaum, 2005. "Weak Dependence Beyond Mixing for Infinite ARCH-type Bilinear Models," Working Papers 2005-50, Center for Research in Economics and Statistics.
    8. Jean‐Marc Bardet & Paul Doukhan & José Rafael León, 2008. "Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 906-945, September.
    9. P. Chigansky & Yu. Kutoyants, 2013. "Estimation in threshold autoregressive models with correlated innovations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 959-992, October.
    10. Hélène Cossette & Etienne Marceau & Véronique Maume-Deschamps, 2011. "Adjustment Coefficient for Risk Processes in Some Dependent Contexts," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 695-721, December.
    11. Giuliano-Antonini, R. & Weber, M., 2008. "The theta-dependence coefficient and an Almost Sure Limit Theorem for random iterative models," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 564-575, April.
    12. Manel Kacem & Stéphane Loisel & Véronique Maume-Deschamps, 2016. "Some mixing properties of conditionally independent processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1241-1259, March.
    13. Sancetta, Alessio, 2005. "Distance between nonidentically weakly dependent random vectors and Gaussian random vectors under the bounded Lipschitz metric," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 158-168, December.
    14. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    15. Jerôme Dedecker & Paul Doukhan, 2002. "A New Covariance Inequality and Applications," Working Papers 2002-25, Center for Research in Economics and Statistics.
    16. Hwang, Eunju & Shin, Dong Wan, 2014. "Infinite-order, long-memory heterogeneous autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 339-358.
    17. Guessoum, Zohra & Ould Saïd, Elias & Sadki, Ourida & Tatachak, Abdelkader, 2012. "A note on the Lynden-Bell estimator under association," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1994-2000.
    18. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Paul Doukhan & Gabriel Lang & Anne Leucht & Michael H. Neumann, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 290-314, May.
    19. Jirak, Moritz, 2012. "Change-point analysis in increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 136-159.
    20. Christophe Cuny & Jérôme Dedecker & Florence Merlevède, 2024. "Strong Approximations for a Class of Dependent Random Variables with Semi-Exponential Tails," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2234-2252, September.

    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:117:y:2007:i:7:p:878-903. 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.