A BERNSTEIN-VON MISES THEOREM FOR DOUBLY CENSORED DATA

We prove a Bernstein-von Mises theorem for the survival function based on doubly censored data. In particular, we develop a new technique for proving Bernstein-von Mises theorems for nonparametric problems. We consider two Bayesian approaches for doubly censored data: the direct approach, where we obtain the posterior of the distribution of the survival times by putting the Dirichlet process prior on the distribution of the survival times; an indirect approach, where we first obtain the posterior of the distribution of the observables with the Dirichlet process and from which we get the posterior of the distribution of the survival times. We show that the two posterior distributions from these two approaches are the same. Using this fact, we prove a Bernstein-von Mises theorem.