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Strong embedding of the estimator of the distribution function under random censorship. (English) Zbl 0667.62024
The present paper is concerned with a strong approximation result for the product limit estimator processes \(\sqrt{n}(F_ n-F)\), where \(F_ n\) is the product limit estimator of an unknown distribution function F based on \((Z_ i;\delta_ i)\) with \(Z_ i=\min (X_ i,Y_ i)\) and \(\delta_ i=I(X_ i\leq Y_ i)\), \(i=1,...,n\), given two independent sequences \(X_ 1,...,X_ n\) and \(Y_ 1,...,Y_ n\) of i.i.d. random variables with df. F and G, respectively. By approximating \(\sqrt{n}\) \((F_ n-F)\) by a certain linear functional of an empirical process at an appropriate rate, it is shown that the rate of strong approximation for the product limit estimator processes by a sequence of Gaussian processes is as good as in the special case when there is no censoring.
Reviewer: P.Gaenssler

62G05 Nonparametric estimation
62F15 Bayesian inference
60F17 Functional limit theorems; invariance principles
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