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Strong Approximation Theorems for Independent Random Variables and Their Applications

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  • Shao, Q. M.

Abstract

This paper provides an elementary way to establish the general strong approximation theorems for independent random variables by using two special results of Sakhanenko. Applications to the law of the iterated logarithm and the strong law of large numbers are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:52:y:1995:i:1:p:107-130
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    Cited by:

    1. Hidalgo, Javier & Seo, Myung Hwan, 2013. "Testing for structural stability in the whole sample," Journal of Econometrics, Elsevier, vol. 175(2), pages 84-93.
    2. Chang, Yoosoon, 2004. "Bootstrap unit root tests in panels with cross-sectional dependency," Journal of Econometrics, Elsevier, vol. 120(2), pages 263-293, June.
    3. repec:cep:stiecm:/2011/558 is not listed on IDEAS
    4. 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.
    5. repec:cep:stiecm:em/2011/558 is not listed on IDEAS
    6. Raluca Balan & Kulik, 2005. "Self-Normalized Weak Invariance Principle for Mixing Sequences," RePAd Working Paper Series lrsp-TRS417, Département des sciences administratives, UQO.
    7. repec:cep:stiecm:em/2013/561 is not listed on IDEAS
    8. repec:cep:stiecm:/2013/561 is not listed on IDEAS
    9. 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.
    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. 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.

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