2020, 10 : 21-27
Published online 2020 October 23. DOI: 10.2174/2666148902010010021
Publisher ID: TOSPJ-10-21

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

Qiqing Yu¹^{, *}

^*Address correspondence to this author at the Department of Mathematical Sciences, SUNY, Binghamton, NY, 13902, USA; E-mail: qyu@math.binghamton.edu

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.

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