Kullback–Leibler information of a censored variable and its applications

Abstract

In this paper, we study the Kullback–Leibler (KL) information of a censored variable, which we will simply call it censored KL information. The censored KL information is shown to have the necessary monotonicity property in addition to inherent properties of nonnegativity and characterization. We also present a representation of the censored KL information in terms of the relative risk and study its relation with the Fisher information in censored data. Finally, we evaluate the estimated censored KL information as a goodness-of-fit test statistic.

Keywords:

• Fisher information
• goodness-of-fit test
• hazard function
• survival analysis

Acknowledgements

The authors are grateful to an anonymous referee and the associate editor for providing some useful comments on an earlier version of this manuscript. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0029104, 2012-004905).