A semiparametric estimator of the bivariate distribution function for censored gap times

Let (T(1), T(2)) be gap times corresponding to two consecutive events, which are observed subject to random right-censoring. In this paper, a semiparametric estimator of the bivariate distribution function of (T(1), T(2)) and, more generally, of a functional E [φ(T(1),T(2))] is proposed. We assume that the probability of censoring for T(2) given the (possibly censored) gap times belongs to a parametric family of binary regression curves. We investigate the conditions under which the introduced estimator is consistent. We explore the finite sample behavior of the estimator and of its bootstrap standard error through simulations. The main conclusion of this paper is that the semiparametric estimator may be much more efficient than purely nonparametric methods. Real data illustration is included.