Estimation of the conditional distribution in regression with censored data: a comparative study

Abstract

In nonparametric regression with censored data, the conditional distribution of the response given the covariate is usually estimated by the Beran (Technical Report, University of California, Berkeley, 1981) estimator. This estimator, however, is inconsistent in the right tail of the distribution when heavy censoring is present. In an attempt to solve this inconsistency problem of the Beran estimator, Van Keilegom and Akritas (Ann. Statist. (1999)) developed an alternative estimator for heteroscedastic regression models (see (1.1) below for the definition of the model), which behaves well in the right tail even under heavy censoring. In this paper, the finite sample performance of the estimator introduced by Van Keilegom and Akritas (Ann. Statist. (1999)) and the Beran (Technical Report, University of California, Berkeley, 1981) estimator is compared by means of a simulation study. The simulations show that both the bias and the variance of the former estimator are smaller than that of the latter one. Also, these estimators are used to analyze the Stanford heart transplant data.