IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v81y1999i1p81-101.html
   My bibliography  Save this article

Convergence of weighted partial sums when the limiting distribution is not necessarily Radon

Author

Listed:
  • Csörgo, Miklós
  • Norvaisa, Rimas
  • Szyszkowicz, Barbara

Abstract

Let be a non-separable Banach space of real-valued functions endowed with a weighted sup-norm. We consider partial sum processes as random functions with values in . We establish weak convergence statements for these processes via their weighted approximation in probability by an appropriate sequence of Gaussian random functions. The main result deals with convergence of distributions of certain functionals in the case when the Wiener measure is not necessarily a Radon measure on .

Suggested Citation

  • 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.
  • Handle: RePEc:eee:spapps:v:81:y:1999:i:1:p:81-101
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(98)00100-8
    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. Shao, Q. M., 1995. "Strong Approximation Theorems for Independent Random Variables and Their Applications," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 107-130, January.
    2. 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.
    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. Chang, Yoosoon, 2004. "Bootstrap unit root tests in panels with cross-sectional dependency," Journal of Econometrics, Elsevier, vol. 120(2), pages 263-293, June.
    2. Glynn, Peter W. & Wang, Rob J., 2023. "A heavy-traffic perspective on departure process variability," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    3. Hidalgo, Javier & Seo, Myung Hwan, 2013. "Testing for structural stability in the whole sample," Journal of Econometrics, Elsevier, vol. 175(2), pages 84-93.
    4. 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.
    5. 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.
    6. 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.
    7. repec:cep:stiecm:/2011/558 is not listed on IDEAS
    8. Bashtova, Elena & Shashkin, Alexey, 2022. "Strong Gaussian approximation for cumulative processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1-18.
    9. repec:cep:stiecm:em/2013/561 is not listed on IDEAS
    10. Menshikov, M.V. & Wade, Andrew R., 2008. "Logarithmic speeds for one-dimensional perturbed random walks in random environments," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 389-416, March.
    11. 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.
    12. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    13. 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.
    14. Jirak, Moritz, 2013. "A Darling–Erdös type result for stationary ellipsoids," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1922-1946.
    15. Timothy B Armstrong & Michal Kolesár, 2018. "A Simple Adjustment for Bandwidth Snooping," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 732-765.
    16. M. A. Lifshits & M. Weber, 1997. "Strassen Laws of Iterated Logarithm for Partially Observed Processes," Journal of Theoretical Probability, Springer, vol. 10(1), pages 101-115, January.
    17. 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.
    18. Raluca Balan & Kulik, 2005. "Self-Normalized Weak Invariance Principle for Mixing Sequences," RePAd Working Paper Series lrsp-TRS417, Département des sciences administratives, UQO.
    19. repec:cep:stiecm:/2013/561 is not listed on IDEAS
    20. Vogel, Quirin, 2021. "A note on the intersections of two random walks in two dimensions," Statistics & Probability Letters, Elsevier, vol. 178(C).
    21. 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.
    22. 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.
    23. 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.

    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:81:y:1999:i:1:p:81-101. 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.