RESEARCH ARTICLE
Consistency of the Semi-parametric MLE under the Cox Model with Right-Censored Data
Qiqing Yu1, *
Article Information
Identifiers and Pagination:
Year: 2020Volume: 10
First Page: 21
Last Page: 27
Publisher Id: TOSPJ-10-21
DOI: 10.2174/2666148902010010021
Article History:
Received Date: 14/05/2020Revision Received Date: 14/08/2020
Acceptance Date: 19/08/2020
Electronic publication date: 23/10/2020
Collection year: 2020
© 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: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Abstract
Objective:
We studied the consistency of the semi-parametric maximum likelihood estimator (SMLE) under the Cox regression model with right-censored (RC) data.
Methods:
Consistency proofs of the MLE are often based on the Shannon-Kolmogorov inequality, which requires finite E(lnL), where L is the likelihood function.
Results:
The results of this study show that one property of the semi-parametric MLE (SMLE) is established.
Conclusion:
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).
