Abstract

Density and hazard estimation in censored regression models

I. VAN KEILEGOM and N. VERAVERBEKE

Let (X,Y) be a random vector, where Y denotes the variable of interest, possibly subject to random right censoring, and X is a covariate. Consider a heteroscedastic model Y=m(X)+s (X)e, where the error term e is independent of X and m(X) and s (X) are smooth but unknown functions. Under this model, we construct a nonparametric estimator for the density and hazard function of Y given X, which has a faster rate of convergence than the completely nonparametric estimator that is constructed without making any model assumption. Moreover, the proposed estimator for the density and hazard function performes better than the classical nonparametric estimator, especially in the right tail of the distribution.

We prove the weak convergence of both the density and the hazard function estimator. The results are obtained by constructing asymptotic representations for the two estimators and by making use of work by Van Keilegom and Akritas in which an estimator of the conditional distribution of Y given X is studied under the same model assumption.

  Last update: January, 24, 2003  - Contact : S. Malali