Consistency of the Semi-parametric MLE under the Cox Model with Right-Censored Data

Qiqing Yu1, *
1 Department of Mathematical Sciences, SUNY, Binghamton, NY, 13902, USA

© 2020 Qiqing Yu.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Mathematical Sciences, SUNY, Binghamton, NY, 13902, USA; E-mail:



We studied the consistency of the semi-parametric maximum likelihood estimator (SMLE) under the Cox regression model with right-censored (RC) data.


Consistency proofs of the MLE are often based on the Shannon-Kolmogorov inequality, which requires finite E(lnL), where L is the likelihood function.


The results of this study show that one property of the semi-parametric MLE (SMLE) is established.


Under the Cox model with RC data, E(lnL) may not exist. We used the Kullback-Leibler information inequality in our proof.

Keywords: Cox model, Maximum likelihood estimator, Consistency, Kullback-Leibler Inequality, Shannon-Kolmogorov inequality, Without loss of generality (WLOG).