Uniform Consistency for Conditional Lifetime Distribution Estimators Under Random Right- Censorship

摘要

We define nonparametric kernel-type estimators of the conditional distribution of a lifetime, in a random censorship framework. We show that these estimators have closed-form expressions, and establish their strong uniform consistency under minimal assumptions. The present work is concerned with the estimation of a conditional lifetime distribution under random censorship from the right. The model we consider is based upon a sequence of observations (X_n, Y_n, U_n), n = 1,2,..., of a random vector (X,Y,U), where X denotes a positive lifetime of interest, Y a positive censoring time, and U a concomitant variable whose influence on the distributions of X and Y is to be assessed. Throughout, we will assume that X and Y are conditionally mutually independent, given U.