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Asymptotic properties of conditional quantile estimator for censored dependent observations

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Abstract

In this paper, we establish strong uniform convergence and asymptotic normality of the conditional quantile estimator for the censorship model when the data exhibit some kind of dependence. It is assumed that the observations form a stationary α-mixing sequence. The strong uniform convergence in iid framework has recently been discussed by Ould-Saïd (Stat Probab Lett 76:579–586, 2006). As a by-product, we also obtain a uniform weak convergence rate for the product-limit estimator of the lifetime and censoring distributions under dependence, which is interesting independently.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, 200092, Shanghai, People’s Republic of China

    Han-Ying Liang

  2. Department of Statistics and Operations Research, Facultad de Ciencias Económicas y Empresariales, Universidad de Vigo, Campus Lagoas-Marcosende, 36310, Vigo, Spain

    Han-Ying Liang & Jacobo de Uña-Álvarez

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  1. Han-Ying Liang
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  2. Jacobo de Uña-Álvarez
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Correspondence to Han-Ying Liang.

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Liang, HY., de Uña-Álvarez, J. Asymptotic properties of conditional quantile estimator for censored dependent observations. Ann Inst Stat Math 63, 267–289 (2011). https://doi.org/10.1007/s10463-009-0230-8

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  • DOI: https://doi.org/10.1007/s10463-009-0230-8

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