IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v28y1989i1p20-68.html
   My bibliography  Save this article

Extensions of results of Komlós, Major, and Tusnády to the multivariate case

Author

Listed:
  • Einmahl, Uwe

Abstract

A construction method is developed which enables us to establish the well-known approximation results of Komlós, Major, Tusnády (Z. Wahrsch. Verw. Gebiete34 33-58) in the multidimensional setting. The basic tool is a large deviation theorem for conditional distribution functions which may be of independent interest.

Suggested Citation

  • Einmahl, Uwe, 1989. "Extensions of results of Komlós, Major, and Tusnády to the multivariate case," Journal of Multivariate Analysis, Elsevier, vol. 28(1), pages 20-68, January.
    • Handle: RePEc:eee:jmvana:v:28:y:1989:i:1:p:20-68
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(89)90097-3
    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. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    2. Cao, Guanqun & Wang, Li, 2018. "Simultaneous inference for the mean of repeated functional data," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 279-295.
    3. S{o}ren Johansen & Morten {O}rregaard Nielsen, 2022. "Weak convergence to derivatives of fractional Brownian motion," Papers 2208.02516, arXiv.org, revised Oct 2022.
    4. Jingjia Liu & Quirin Vogel, 2021. "Large Deviations of the Range of the Planar Random Walk on the Scale of the Mean," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2315-2345, December.
    5. Glynn, Peter W. & Wang, Rob J., 2023. "A heavy-traffic perspective on departure process variability," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    6. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
    7. Yuzo Hosoya, 2005. "Fractional Invariance Principle," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 463-486, May.
    8. Vogel, Quirin, 2021. "A note on the intersections of two random walks in two dimensions," Statistics & Probability Letters, Elsevier, vol. 178(C).
    9. Csörgo, Miklós & Horváth, Lajos, 1996. "A note on the change-point problem for angular data," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 61-65, March.
    10. Amir, Gideon & Benjamini, Itai & Gurel-Gurevich, Ori & Kozma, Gady, 2020. "Random walk in changing environment," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7463-7482.
    11. Jirak, Moritz, 2013. "A Darling–Erdös type result for stationary ellipsoids," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1922-1946.
    12. Koval, Valery & Schwabe, Rainer, 2003. "A law of the iterated logarithm for stochastic approximation procedures in d-dimensional Euclidean space," Stochastic Processes and their Applications, Elsevier, vol. 105(2), pages 299-313, June.
    13. Park, Joon Y. & Shin, Kwanho & Whang, Yoon-Jae, 2010. "A semiparametric cointegrating regression: Investigating the effects of age distributions on consumption and saving," Journal of Econometrics, Elsevier, vol. 157(1), pages 165-178, July.
    14. Liu, Weidong & Lin, Zhengyan, 2009. "Strong approximation for a class of stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 249-280, January.
    15. M. Kayid & M. Shafaei Noughabi & A. M. Abouammoh, 2020. "A Nonparametric Estimator of Bivariate Quantile Residual Life Model with Application to Tumor Recurrence Data Set," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 237-253, April.
    16. Arup Bose & Rajat Subhra Hazra & Koushik Saha, 2011. "Spectral Norm of Circulant-Type Matrices," Journal of Theoretical Probability, Springer, vol. 24(2), pages 479-516, June.
    17. Csörgo, Miklós & Norvaisa, Rimas & Szyszkowicz, Barbara, 1999. "Convergence of weighted partial sums when the limiting distribution is not necessarily Radon," Stochastic Processes and their Applications, Elsevier, vol. 81(1), pages 81-101, May.
    18. Bashtova, Elena & Shashkin, Alexey, 2022. "Strong Gaussian approximation for cumulative processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1-18.

    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:jmvana:v:28:y:1989:i:1:p:20-68. 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/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.