A SIMPLE NONPARAMETRIC ESTIMATOR OF THE BIVARIATE SURVIVAL FUNCTION UNDER UNIVARIATE CENSORING

In the presence of univariate censoring, the bivariate survival functi on of paired failure times can be expressed as the ratio of the bivari ate at-risk probability to the survival function of the censoring time . The use of this natural representation yields a very simple nonparam etric estimator for the bivariate survival curve. The estimator is str ongly consistent and, upon proper normalization, converges weakly to a zero-mean Gaussian process with an easily estimated covariance functi on. Numerical studies demonstrate that both the survival curve estimat or and its covariance function estimator perform markedly well for pra ctical sample sizes. Applications to the correlation problem and to th e interval estimation of the difference in median survival times are a lso studied.