统计与数据科学系系列学术报告之四百一十四期

时   间：2023年11月28日（周二）14:00-15:00

地   点：史带楼501室

主持人：复旦大学 管理学院 统计与数据科学系 张新生 教授

报告人：Professor Bin Nan  Chancellor’s Professor, Department of Statistics, UCI

题   目：Statistical Inference for Nonlinear Regression Models with High-Dimensional Covariates

摘   要：For statistical inference on regression models with large numbers of covariates, the existing literature on debiased lasso typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often violated particularly for nonlinear regression models such as generalized linear models, leading to biased estimates with under-coverage confidence intervals. We propose to tackle this problem in two different situations: (1) When the number of covariates $p$ increases with the sample size $n$, but less than $n$, we modify the debiased lasso approach by directly inverting the information matrix without posing sparse matrix assumptions; (2) When $p>n$, we implement the sample splitting method where we select a submodel via lasso using part of the original data and then fit the selected model via the debiased method in (1) using the remaining data. We establish asymptotic results for the estimated regression coefficients. As demonstrated by extensive simulations, our proposed methods provide consistent estimates and confidence intervals with nominal coverage probabilities. This is joint work with Omar Vazquez, Lu Xia and Yi Li.

个人简介：Bin Nan 教授是美国统计学会（ASA）和国际数理统计学会（IMS）的Fellow、以及国际统计研究会（ISI）Elected Member. 在JASA，AOS，AOAS，Biometrika等国际期刊上发表论文超过100篇，他的研究兴趣主要集中在生存分析、高维大脑图像的数据分析、纵向数据的变点分析等研究领域。

统计与数据科学系

2023-11-21