Nonparametric Bayesian estimation of a survival function under the proportional hazard model

Let X1,...,Xn be the true survival times of n individuals which are randomly censored on the right by Y1,...,Yn. Let SX and SY be the survival function of X and Y respectively. Under the proportional hazard model for some β > 0. Assuming a Dirichlet process prior, D(α), for SX an estimator is derived. These estimators are the Bayesian extension of the maximum likelihood estimator derived by Abduskhurov(1984) and Cheng and Lin (1984,1987). It is shown that these estimators are mean square consistent, almost sure consistent and converge to a zero mean Gaussian process on finite intervals. A numerical example is presented to illustrate the estimator.