zbMATH — the first resource for mathematics

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

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