Robust and efficient parameter estimation based on censored data with stochastic covariates

ABSTRACT

Analysis of random censored life-time data along with some related stochastic covariables is of great importance in many applied sciences. 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 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 real data example and simulation studies. 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.

Keywords:

• Censored data
• robust methods
• linear regression
• density power divergence
• M-estimator
• exponential regression model
• accelerated failure time model

Acknowledgments

The authors gratefully acknowledge the comments of the anonymous referees and the associate editor which led to an improved version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Abhik Ghosh http://orcid.org/0000-0003-3688-4584