Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	刘妍岩博士，武汉大学数学与统计学院
Inviter:	孙六全副研究员
Title:	Functional Martingale Residual Process for High-Dimensional Cox Regression with Model Averaging
Time & Venue:	2019.7.1 15:00 N702
Abstract:	Regularization methods for the Cox proportional hazards regression with high-dimensional survival data have been studied extensively in the literature. However, if the models are misspecified, this would result in misleading statistical inference and prediction. To enhance the prediction accuracy for the relative risk and the survival probability of clinical interest, we propose three model averaging approaches for the high-dimensional Cox proportional hazards regression. Based on the martingale residual process, we define the delete-one crossvalidation process. Further, we propose three novel cross-validation functionals, including the end-time cross-validation, integrated cross-validation, and supremum cross-validation, to achieve more accurate prediction for the risk quantities. The optimal weights for candidate models, without the constraint of summing up to one, can be obtained by minimizing these functionals, respectively. The proposed model averaging approaches can attain the lowest possible prediction loss asymptotically. Furthermore, we develop a greedy model averaging algorithm to overcome the computational obstacle when the dimension is high. The performance of the proposed model averaging procedures is evaluated via extensive simulation studies, showing that our methods have superior prediction accuracy over the existing regularization methods. As an illustration, we apply the proposed methods to the mantle cell lymphoma study.