# zbMATH — the first resource for mathematics

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

##### MSC:
 62G05 Nonparametric estimation 62F15 Bayesian inference 60F17 Functional limit theorems; invariance principles
Full Text: