Consistency of self-consistent estimators of a discrete distribution function with bivariate right-censored data
The asymptotic propertics of the nonparmetric maximum likelihood estimater and other estimators of a joint distribution function F of a bivariate random vector X with right-censored data have been studied by several authors. Among others, an important assumption made in their studies is that X lives on a rectangle region [0, a] × [0, b] which can be observed. However, in many follow-up studiesa = b= L is the length of the study period and X lives on a region larger man [0, L] × [0, L]. Thus it is of interest to study whether the asymptotic results established bv these authors are still valid without that restriction. In this direction, we established the strong consistence of self-consistent estimators of a discrete distribution function.