ABSTRACT
This chapter considers the long-standing statistical problem of nonparametric estimation of the bivariate survivor function (F). The F estimator that arises from plugging empirical marginal single and double failure hazard estimators into a corresponding representation for F, however, has a distracting feature; namely, the estimator typically incorporates negative mass assignments. The chapter explores some additional approaches to the estimation of F, and provides a general perspective on bivariate hazard rate and survivor function estimation. While the Volterra estimator has the desirable asymptotic properties that one might expect from its empirical single failure and double failure hazard rate components, it also has the distracting feature of typically incorporating negative probability assignments. Dabrowska and Prentice–Cai estimators use the Kaplan–Meier (KM) marginal survivor function estimators, but do so in conjunction with a double failure estimator that acknowledges the KM estimators to some extent. Both estimators focus on representations for the ratio of F to the product of its corresponding marginal survivor functions.
