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Quantile process for left truncated and right censored data

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Abstract

In this paper, we consider the product-limit quantile estimator of an unknown quantile function when the data are subject to random left truncation and right censorship. 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 product-limit quantile process are constructed with rate\(O(\frac{{(\log n)^{3/2} }}{{n^{1/8} }})\). A functional law of the iterated logarithm for the maximal deviation of the estimator from the estimand is derived from the construction.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Donghua University, Hualien, Taiwan, R.O.C.

    Szeman Tse

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  1. Szeman Tse
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Additional information

Work partially supported by NSC Grant 89-2118-M-259-011.

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Tse, S. Quantile process for left truncated and right censored data. Ann Inst Stat Math 57, 61–69 (2005). https://doi.org/10.1007/BF02506879

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  • DOI: https://doi.org/10.1007/BF02506879

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