Density and hazard estimation in censored regression models

Abstract

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)+σ(X)ε, where the error term ε is independent of X and m(X) and σ(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 performs better than the classical nonparametric estimator, especially in the right tail of the distribution.