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Strong Gaussian approximations of product-limit and quantile processes for truncated data under strong mixing

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  • Ghalibaf, M. Bolbolian
  • Fakoor, V.
  • Azarnoosh, H.A.

Abstract

In this paper, we consider the product-limit quantile estimator of an unknown quantile function under a truncated dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit estimator under the same model. Simultaneous strong Gaussian approximations of the product-limit process and normed product-limit quantile process are constructed with rate O((logn)-[lambda]) for some [lambda]>0. The strong Gaussian approximation of the product-limit process is then applied to derive the law of the iterated logarithm for the product-limit process.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:581-586
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    References listed on IDEAS

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