IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v79y2009i23p2405-2414.html
   My bibliography  Save this article

On the weak laws of large numbers for arrays of random variables

Author

Listed:
  • Meng, Yanjiao
  • Lin, Zhengyan

Abstract

In this paper we obtain weak laws of large numbers (WLLNs) for arrays of random variables under the uniform Cesàro-type condition. As corollary, we obtain the result of Hong and Oh [Hong, D. H., Oh, K. S., 1995. On the weak law of large numbers for arrays. Statist. Probab. Lett. 22, 55-57]. Furthermore, we obtain a WLLN for an Lp-mixingale array without the conditions that the mixingale is uniformly integrable and the Lp-mixingale numbers decay to zero at a special rate.

Suggested Citation

  • Meng, Yanjiao & Lin, Zhengyan, 2009. "On the weak laws of large numbers for arrays of random variables," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2405-2414, December.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:23:p:2405-2414
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00323-X
    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. Li, Yulin, 2003. "A martingale inequality and large deviations," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 317-321, April.
    2. Dug Hun Hong & Kwang Sik Oh, 1995. "On the weak law of large numbers for arrays," Statistics & Probability Letters, Elsevier, vol. 22(1), pages 55-57, January.
    3. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
    Full references (including those not matched with items on IDEAS)

    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. Meng, Yanjiao & Lin, Zhengyan, 2009. "Maximal inequalities and laws of large numbers for Lq-mixingale arrays," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1539-1547, July.
    2. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    3. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2001. "Comparing dynamic equilibrium economies to data," FRB Atlanta Working Paper 2001-23, Federal Reserve Bank of Atlanta.
    4. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1500-1529, December.
    5. Koo, Bonsoo & Seo, Myung Hwan, 2015. "Structural-break models under mis-specification: Implications for forecasting," Journal of Econometrics, Elsevier, vol. 188(1), pages 166-181.
    6. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2017. "Correction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 883-883, April.
    7. Fiteni, Inmaculada, 2004. "[tau]-estimators of regression models with structural change of unknown location," Journal of Econometrics, Elsevier, vol. 119(1), pages 19-44, March.
    8. Rajae Azrak & Guy Mélard, 2022. "Autoregressive Models with Time-Dependent Coefficients—A Comparison between Several Approaches," Stats, MDPI, vol. 5(3), pages 1-21, August.
    9. Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Value at Risk by Quantile Regression," NBER Working Papers 7341, National Bureau of Economic Research, Inc.
    10. Adler, André & Rosalsky, Andrew & Volodin, Andrej I., 1997. "A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 167-174, March.
    11. de Jong, Robert M. & Woutersen, Tiemen, 2011. "Dynamic Time Series Binary Choice," Econometric Theory, Cambridge University Press, vol. 27(4), pages 673-702, August.
    12. Gonçalves, Sílvia & White, Halbert, 2002. "The Bootstrap Of The Mean For Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1367-1384, December.
    13. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
    14. Itai Arieli & Manuel Mueller-Frank, 2019. "Multidimensional Social Learning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 913-940.
    15. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
    16. Kanaya, Shin, 2017. "Convergence Rates Of Sums Of Α-Mixing Triangular Arrays: With An Application To Nonparametric Drift Function Estimation Of Continuous-Time Processes," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1121-1153, October.
    17. Park Joon Y. & Whang Yoon-Jae, 2005. "A Test of the Martingale Hypothesis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(2), pages 1-32, June.
    18. Prono, Todd, 2011. "When A Factor Is Measured with Error: The Role of Conditional Heteroskedasticity in Identifying and Estimating Linear Factor Models," MPRA Paper 33593, University Library of Munich, Germany.
    19. Boldea, Otilia & Cornea-Madeira, Adriana & Hall, Alastair R., 2019. "Bootstrapping structural change tests," Journal of Econometrics, Elsevier, vol. 213(2), pages 359-397.
    20. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2022. "Regularized estimation of high‐dimensional vector autoregressions with weakly dependent innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 532-557, July.

    More about this item

    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:79:y:2009:i:23:p:2405-2414. 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.