A Generalized Kaplan-Meier Estimator

In the theory of competing risks, the nonparametric Kaplan-Meier estimator plays an important role. In this paper, a bivariate nonparametric estimator for the competing risk problem is given, which for the special case of independent causes gives the Kaplan-Meier estimator. This paper also introduces a matrix w, through which dependent models for the competing problem can be studied. These results also indicate the special case on the matrix w for which the bounds to the survival function given by Peterson [4] can be obtained.