AISM 53, 730-745

© 2001 ISM

## Hazard rate estimation in nonparametric regression with censored data

### Ingrid Van Keilegom^{1} and Noël Veraverbeke^{2}

^{1}Institut de Statistique, Université catholique de
Louvain, Voie du Roman Pays 20, B-1348 Louvain-la-Neuve, Belgium

^{2}Department of Mathematics, Limburgs Universitair
Centrum, Universitaire Campus, B-3590 Diepenbeek, Belgium

(Received March 21, 2000; revised September 25, 2000)

Abstract.
Consider a regression model in which the responses are subject to random right censoring.
In this model, Beran studied the nonparametric estimation of the conditional cumulative
hazard function and the corresponding cumulative distribution function. The main idea is
to use smoothing in the covariates. Here we study asymptotic properties of the
corresponding hazard function estimator obtained by convolution smoothing of
Beran's cumulative hazard estimator. We establish asymptotic expressions for the
bias and the variance of the estimator, which together with an asymptotic representation
lead to a weak convergence result. Also, the uniform strong consistency of the
estimator is obtained.

Key words and phrases:
Asymptotic representation, hazard rate, nonparametric regression, right censoring, weak convergence.

**Source**
(TeX , DVI )