报告题目：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 misspecified, this would exert adverse effect on result in misleading statistical inference and prediction. To enhance the prediction accuracy for the relative risk and the survival probability, 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 of clinical interest. 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 approach 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 performances of the proposed model averaging procedures are evaluated via extensive simulation studies, showing that our methods achieve superior prediction accuracy over the existing regularization method. As an illustration, we apply the proposed methods to the mantle cell lymphoma study.
报告人概况：中南财经政法大学统计与数学学院教授、博士生导师。吴远山教授博士毕业于武汉大学，研究方向为高维数据分析; 生存分析。主持多项国家级和省部级科研项目。现已在统计方向顶级期刊Journal of the American Statistical Association，Biometrik，Biometrics等发表学术论文20余篇。