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A note on strong approximation for quantile processes of strong mixing sequences


  • Yu, Hao


In this note we give a short proof that a quantile process based on strong mixing sequences can be approximated by a Gaussian process almost surely. Our result improves Theorem 2 of Fotopoulos et al. (1994), with lighter strong mixing decay rate and wider intervals.

Suggested Citation

  • Yu, Hao, 1996. "A note on strong approximation for quantile processes of strong mixing sequences," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 1-7, September.
  • Handle: RePEc:eee:stapro:v:30:y:1996:i:1:p:1-7

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    References listed on IDEAS

    1. Fotopoulos, S. B. & Ahn, S. K., 1994. "Strong Approximation of the Quantile Processes and Its Applications under Strong Mixing Properties," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 17-45, October.
    2. Babu, Gutti Jogesh & Singh, Kesar, 1978. "On deviations between empirical and quantile processes for mixing random variables," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 532-549, December.
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    Cited by:

    1. Ghalibaf, M. Bolbolian & Fakoor, V. & Azarnoosh, H.A., 2010. "Strong Gaussian approximations of product-limit and quantile processes for truncated data under strong mixing," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 581-586, April.
    2. Ajami, M. & Fakoor, V. & Jomhoori, S., 2011. "The Bahadur representation for kernel-type estimator of the quantile function under strong mixing and censored data," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1306-1310, August.


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