Consistency of the GMLE with mixed case interval-censored data

In this paper we consider an interval censorship model in which the endpoin ts of the censoring intervals are determined by a two stage experiment. In the first stage the value k of a random integer is selected; in the second stage the endpoints are determined by a case k interval censorship model. W e prove the strong consistency in the L-1(mu)-topology of the non-parametri c maximum likelihood estimate of the underlying survival function for a mea sure mu which is derived from the distributions of the endpoints. This cons istency result yields strong consistency for the topologies of weak converg ence, pointwise convergence and uniform convergence under additional assump tions. These results improve and generalize existing ones in the literature .