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Strong approximations of the quantile process of the product-limit estimator

Emad-Eldin A. A. Aly, Miklós Csörgo and Lajos Horvath

Journal of Multivariate Analysis, 1985, vol. 16, issue 2, 185-210

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.

Keywords: Censored; data; product; limit; quantile; process; weak; convergence; strong; approximation; confidence; bands (search for similar items in EconPapers)
Date: 1985
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