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Self-Normalized Weak Invariance Principle for Mixing Sequences

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Author Info

  • Raluca Balan

    ()
    (University of Ottawa, LRSP)

  • Kulik

    ()
    (Wroclaw University and University of Ottawa)

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    Abstract

    In this article we give a necessary and su±cient condition for a selfnormalized weak invariance principle, in the case of a strictly stationary Á-mixing sequence fXjgj¸1. This is obtained under the assumptions that the function L(x) = EX2 1 1fjX1·xg is slowly varying at 1 and the mixing coe±cients satisfy Á1=2(n)

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    File URL: http://www.repad.org/ca/on/lrsp/TRS417.pdf
    File Function: First version, 2005
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    Bibliographic Info

    Paper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number lrsp-TRS417.

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    Length: 15 pages
    Date of creation: 30 Mar 2005
    Date of revision:
    Handle: RePEc:pqs:wpaper:082006

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    Keywords: Self-normalized; weak invariance principle; mixing sequences.;

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    References

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    1. Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
    2. 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.
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    Cited by:
    1. Kulik, Rafal, 2006. "Limit theorems for self-normalized linear processes," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1947-1953, December.

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