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Local convergence of empirical measures in the random censorship situation with application to density and rate estimators. (English) Zbl 0612.62058
The author studies the local deviations of the empirical measure defined by the Kaplan-Meier estimator for the survival function. These results are applied to kernel estimators for the density function f and the hazard rate h. In a general form, these estimators may be written as $f_ n(x)=\int R_ n^{-1}(t)K((x-t)/R_ n(t))dF_ n(t)$ where K is a kernel function integrating to 1 and $R_ n(t)=\inf \{r>0| \quad F_ n(t-r/2)-F_ n(t+r/2)\geq p_ n\},$ $$p_ n\to 0$$ is a sequence of positive real numbers.
Reviewer: V.D.Konakov

##### MSC:
 62G05 Nonparametric estimation 62E20 Asymptotic distribution theory in statistics 62P10 Applications of statistics to biology and medical sciences; meta analysis
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