Strong approximations of the quantile process of the product-limit estimator |
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Authors: | Emad-Eldin A.A Aly Miklós Csörgő Lajos Horváth |
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Affiliation: | 1. Department of Mathematics and Statistics, Carleton University, Canada;2. Department of Statistics, The University of Alberta, Edmonton, Canada;4. Bolyai Institute, Szeged University, Hungary |
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Abstract: | The quantile process of the product-limit estimator (PL-quantile process) in the random censorship model from the right is studied via strong approximation methods. Some almost sure fluctuation properties of the said process are studied. Sections 3 and 4 contain strong approximations of the PL-quantile process by a generalized Kiefer process. The PL and PL-quantile processes by the same appropriate Kiefer process are approximated and it is demonstrated that this simultaneous approximation cannot be improved in general. Section 5 contains functional LIL for the PL-quantile process and also three methods of constructing confidence bands for theoretical quantiles in the random censorship model from the right. |
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Keywords: | 62G15 62G10 62E20 Censored data product limit quantile process weak convergence strong approximation confidence bands |
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