Title： Functional Martingale Residual Process for High-Dimensional Cox Regression with Model Averaging
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 mis-specified, 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 cross validation 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.
刘妍岩 武汉大学数学与统计学院教授，博士生导师。2001年获武汉大学理学博士学位。主要研究方向为生存分析、半参数统计推断、复杂高维数据模型结构选择以及大数据统计分析技术等。曾到美国北卡来罗纳大学教堂山分校、加拿大Simon-Fraser大学、香港理工大学、香港中文大学、德国Greifswald大学等学校短期访问和工作。主持完成国家自然科学基金以及教育部基金项目6项，在统计学期刊 Journal of Machine Learning Research, Biometrics, Biostatistics, Genetics，Lifetime Data Analysis等期刊发表SCI研究论文六十余篇。目前担任国际统计学期刊statistical papers 副主编，数理统计与管理副主编（2022.01-2025.12）,中国现场统计学会第十一届理事会常务理事、中国数学会女专家工作委员会委员,全国应用统计专业学位研究生教育指导委员会委员。
报告时间：2023年9月21日（周四）上午10:00
报告地点：一综B座316