IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v26y1987ip73-85.html
   My bibliography  Save this article

On the strong law of large numbers for multivariate martingales

Author

Listed:
  • Kaufmann, Heinz

Abstract

The strong law of large numbers is considered for a multivariate martingale normed by a sequence of square matrices. In particular multivariate martingale extensions of the strong laws of Kolmogorov and Marcinkiewicz-Zygmund are presented. Convergence to zero in L[alpha] is obtained under the same conditions. Norming by powers of the covariance matrix is considered in detail. Results are further used to derive conditions for strong consistency of the least squares estimator in linear regression with multivariate responses. These conditions do not necessarily assume square integrability of errors. They become particularly simple for polynomially bounded regressors. Two examples are treated, including polynomial regression.

Suggested Citation

  • Kaufmann, Heinz, 1987. "On the strong law of large numbers for multivariate martingales," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 73-85.
    • Handle: RePEc:eee:spapps:v:26:y:1987:i::p:73-85
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(87)90051-2
    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. Chan, N.H. & Cheung, Simon K.C. & Wong, Samuel P.S., 2020. "Inference for the degree distributions of preferential attachment networks with zero-degree nodes," Journal of Econometrics, Elsevier, vol. 216(1), pages 220-234.
    2. Valery Koval, 2002. "A New Law of the Iterated Logarithm in Rd with Application to Matrix-Normalized Sums of Random Vectors," Journal of Theoretical Probability, Springer, vol. 15(1), pages 249-257, January.
    3. R. M. Balan & Ioana Schiopu-Kratina, 2004. "Asymptotic Results with Generalized Estimating Equations for Longitudinal data II," RePAd Working Paper Series lrsp-TRS398, Département des sciences administratives, UQO.
    4. Küchler, Uwe & Sørensen, Michael M., 1998. "A note on limit theorems for multivariate martingales," SFB 373 Discussion Papers 1998,45, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Dzhaparidze, K. & Spreij, P., 1989. "On SLLN for martingales with deterministic variation," Serie Research Memoranda 0079, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

    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:26:y:1987:i::p:73-85. 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/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.