  Analysis of random censored life-time data along with some related stochastic
covariables is of great importance in many applied sciences like medical
research, population studies and planning etc. The parametric estimation
technique commonly used under this set-up is based on the efficient but
non-robust likelihood approach. In this paper, we propose a robust parametric
estimator for the censored data with stochastic covariates based on the minimum
density power divergence approach. The resulting estimator also has competitive
efficiency with respect to the maximum likelihood estimator under pure data.
The strong robustness property of the proposed estimator with respect to the
presence of outliers is examined and illustrated through an appropriate
simulation study in the context of censored regression with stochastic
covariates. Further, the theoretical asymptotic properties of the proposed
estimator are also derived in terms of a general class of M-estimators based on
the estimating equation.
