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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. Javier Hidalgo & Myung Hwan Seo, 2012. "Testing for Structural Stability in the Whole Sample," STICERD - Econometrics Paper Series 561, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    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. Javier Hidalgo & Myunghwan Seo, 2011. "Testing For Structural Stability In The Whole Sample," STICERD - Econometrics Paper Series 558, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. repec:cep:stiecm:/2011/558 is not listed on IDEAS
    5. Timothy B. Armstrong & Michal Kolesar, 2014. "A Simple Adjustment for Bandwidth Snooping," Cowles Foundation Discussion Papers 1961R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2015.
    6. Timothy B. Armstrong & Michal Kolesar, 2014. "A Simple Adjustment for Bandwidth Snooping," Cowles Foundation Discussion Papers 1961R3, Cowles Foundation for Research in Economics, Yale University, revised Jun 2017.
    7. repec:cep:stiecm:em/2011/558 is not listed on IDEAS
    8. Hidalgo, Javier & Seo, Myung Hwan, 2013. "Testing for structural stability in the whole sample," Journal of Econometrics, Elsevier, vol. 175(2), pages 84-93.
    9. Raluca Balan & Kulik, 2005. "Self-Normalized Weak Invariance Principle for Mixing Sequences," RePAd Working Paper Series lrsp-TRS417, Département des sciences administratives, UQO.
    10. repec:cep:stiecm:em/2013/561 is not listed on IDEAS
    11. repec:cep:stiecm:/2013/561 is not listed on IDEAS
    12. Timothy B. Armstrong & Michal Kolesar, 2014. "A Simple Adjustment for Bandwidth Snooping," Cowles Foundation Discussion Papers 1961R2, Cowles Foundation for Research in Economics, Yale University, revised Oct 2016.
    13. 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.
    14. 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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