Bayesian Bootstrap Clones for Censored Markov Chains

Abstract

In this article, we consider r observations {(X k n . J k n ), 0 ≤ n ≤ N, k = 1,..., r} from a non-homogeneous censored Markov chain, with transition probability matrix P. For the product estimator P of P proposed by AALEN and JOHANSEN (1978) and PHELAN (1988), we investigate the behavior of Bayesian bootstrap clones to approximate the sampling distribution of √r (P - P), and then construct approximate confidence interval. It is shown that the approximation based on the random-weighted distribution is first-order consistent. The performance of the Bayesian bootstrap clones (BBC) is also discussed by small sample simulation. Finally, we illustrate the BBC procedure in the application to the WHO malaria survey data (cf. SINGER and COHEN 1970).