数学科学学院学术报告[2025] 012号

(高水平大学建设系列报告1035号)

报告题目: Goodness-of-Fit Tests for High-Dimensional Regression Models via  Projections.  

报告人：谭发龙 教授（湖南大学）

报告时间：2025年3月23日下午16:00-17:00

报告地点： 校友广场303会议室                                            

报告内容：In this talk, we proposed a new method for testing the goodness of fit for high dimensional generalized linear regression models when the number of covariates may be much larger than the sample size. Most existing model checking methods in the literature does not work for high dimension regression models as they suffer from the curse of dimensionality and rely on the asymptotic linearity and normality of the estimator of the parameters. Our method is based on random projections which largely avoid the “curse of dimensionality”. Further, our test only need the convergence rate of the estimators of the high dimensional parameters and does not rely on the asymptotic expansion or the normality of these estimators. The asymptotic properties of the test statistics are investigated under the null and the local and global alternatives when the number of covariates is much larger than the sample sizes. We further proposed a combination method to enhance the power performance of the tests. Detailed simulation studies and a real data analysis are conducted to illustrate the effectiveness of our methodology.

报告人简介：谭发龙，现任湖南大学金融与统计学院教授、博士生导师。主要研究兴趣包括人工智能的数学与统计基础、统计机器学习、高维模型检验、高维经验过程、充分性降维、因果推断与精准医疗等。相关研究工作发表在Annals of Statisitcs、Biometrika、CVPR、Statistica Sinica等国际期刊与会议上，主持和参与国家自然科学基金、省部级项目10余项。

欢迎师生参加！

报告邀请人：数学科学学院（周彦）                                            

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　　　　　　　　　　　　　　　　　　 2025年03月17日