深圳大学数学科学学院

荔园学者Colloquium第七十三期

讲座题目: Parsimonious Model Averaging with a Diverging Number of Parameters

主讲人：梁华 教授（乔治•华盛顿大学）

报告时间：2024年1月23日下午16:00-17:00

讲座地点：深圳大学粤海校区汇星楼一楼一号教室

内容概述：Model averaging generally provides better predictions than model selection, but the existing model averaging methods cannot lead to parsimonious models. Parsimony is an especially important property when the number of parameters is large. To achieve a parsimonious model averaging coefficient estimator, we suggest a novel criterion for choosing weights. Asymptotic properties are derived in two practical scenarios: (i) one or more correct models exist in the candidate model set; and (ii) all candidate models are misspecified. Under the former scenario, it is proved that our method can put the weight one to the smallest correct model and the resulting model averaging estimators of coefficients have many zeros and thus lead to a parsimonious model. The asymptotic distribution of the estimators is also provided. Under the latter scenario, prediction is mainly focused on and we prove that the proposed procedure is asymptotically optimal in the sense that its squared prediction loss and risk are asymptotically identical to those of the best but infeasible model averaging estimator. Numerical analysis shows the promise of the proposed procedure over existing model averaging and selection methods.

主讲人简介：梁华， 乔治•华盛顿大学统计系教授,曾任罗切斯特大学医学院教授.研究兴趣包括统计模型选择与模型平均、非参数与半参数回归、爱兹病临床试验与动态建模等。 出版英文学术著作2本，发表学术论文180余篇。主持了8项美国国家科学基金会以及美国国立卫生研究院的研究项目。国家重要人才计划入选者。美国统计学会、国际数理统计学会fellow，曾任JASA等刊物的编委或副主编。

欢迎师生参加！

邀请人：数学科学学院（魏正红）

数学科学学院

2024年1月17日