Abstract

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of <TEX>$F_{\alpha}$</TEX>, he NPBE of F with respect to the Dirichlet process prior D(<TEX>$\alpha$</TEX>), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, <TEX>$\alpha$</TEX>, Hjort(1990) obtained the Bayes estimator <TEX>$A_{c,\alpha}$</TEX> of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator <TEX>$F_{c,\alpha}$</TEX> is recovered from <TEX>$A_{c,\alpha}$</TEX>. Continuity assumption on F and G is removed in our proof of the consistency of <TEX>$A_{c,\alpha}$</TEX> and <TEX>$F_{c,\alpha}$</TEX>. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.