Lifetime estimation from doubly censored data and dirichlet process prior knowledge on the observable random vector

Abstract

The purpose of this paper is to present a nonparametric Bayesian procedure for estimating a survival curve in a double censoring situation. Assuming a proportional hazard rates model, we propose a consistent estimation of lifetime, based on a Dirichlet process prior knowledge on the observable random vector. Some large sample properties of this estimator are also derived, We prove strong consistency and asymptotic weak convergence to a Gaussian pro cess. Finally, a simulation study is presented in order to analyze the behavior of the proposed estimator, and establish some comparisons to other estimators.

Keywords:

• Bayesian nonparametric inference
• proportional hazard models
• right and lefl censoring
• survival function