讲座题目：Unified optimal model averaging with a general loss function based on cross-validation
主讲人：喻达磊 教授
主持人：马慧娟 副教授
开始时间：2025-09-19 16:00
讲座地址：普陀校区理科大楼A1514
主办单位：统计学院
报告人简介：
喻达磊，西安交通大学数学与统计学院教授，博士生导师，入选国家高层次青年人才计划。研究领域为统计预测、估计理论和统计极限理论等，一些成果发表在JRSS-B、JASA、JMLR、JBES和《中国科学：数学》等期刊上。先后主持三项国家自然科学基金项目和一项国家重点研发计划项目课题。
报告内容：
Studying unified model averaging estimation for situations with complicated data structures, we propose a novel model averaging method based on cross-validation (MACV). MACV unifies a large class of new and existing model averaging estimators and covers a very general class of loss functions. Furthermore, to reduce the computational burden caused by the conventional leave-subject/one-out cross validation, we propose a SEcond-order-Approximated Leave-one/subject-out (SEAL) cross validation, which largely improves the computation efficiency. As a useful tool, we extend the Bernstein-type inequality for strongly mixing random variables that are not necessarily identically distributed. In the context of non-independent and non-identically distributed random variables, we establish the unified theory for analyzing the asymptotic behaviors of the proposed MACV and SEAL methods, where the number of candidate models is allowed to diverge with sample size. To demonstrate the breadth of the proposed methodology, we exemplify four optimal model averaging estimators under four important situations, i.e., longitudinal data with discrete responses, within-cluster correlation structure modeling, conditional prediction in spatial data, and quantile regression with a potential correlation structure. We conduct extensive simulation studies and analyze real-data examples to illustrate the advantages of the proposed methods.
