Estimation of a Bivariate Distribution under Univariate Censoring

Abstract

We compare four estimators of a bivariate distribution function H when both components of the data point (X; Y ) are subject to censoring by the same (univariate) random variable C with distribution G. We use the same simulated data to calculate each of the four estimators for 5 di erent FGM copulas. Finally we nd the best of the four estimators, that is the adapted path dependent estimator. We will show that it is not necessarily a good idea to use all the available information about C and that our estimator of H can be improved by using a worse estimator of G. ii