Geometry of exponential family with competing risks and censored data

Employing the differential geometrical methods in statistics suggested by Amari (1985) and Amari et al. (1987), considering the exponential family with censored data and competing risks as a manifold of a statistical model, the geometry of the manifold is investigated based on two information sources. As an application of the geometry, the asymptotic expansions of the bootstrap prediction, Bayesian prediction and their risk evaluations are investigated. The results show that these expansions are related to the coefficients of alpha-connections and metric tensors, and the predictive density function is the estimative density function in the asymptotic sense. Finally, taking Rayleigh distribution and prostatic cancer data as examples, some computation and simulation results are presented to illustrate our main results. (C) 2015 Elsevier B.V. All rights reserved.