Local convergence of empirical measures in the random censorship situation with application to density and rate estimators (Q1088330)

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.