Uncertainty Assessment for Generalized Linear Models via Local Bootstrapping
报告人：李扬 教授 （中国人民大学）
报告时间：2026年05月08日 10:30--11:30
报告地点：数学与统计学院A601报告厅
报告摘要:
Variable selection has been commonly conducted to identify a subset of predictors that significantly contribute to outcomes. Besides obtaining sparse estimates, evaluating estimation uncertainty for parameters is also pivotal. This assessment can be achieved via high-dimensional inference, involving the construction of confidence intervals or hypothesis testing. Different from estimation uncertainty which reflects the variability in parameter estimates, selection uncertainty reflects the variability in the selection of predictors, including its size and composition. Both types of uncertainty can inform the reliability of variable selection procedures. In this article, we use generalized linear models to either approximate or specify the true data generating process. First, a local residual bootstrap (LRB) is introduced to approximate the distribution of high-dimensional penalized estimates encompassing all values of the regression parameter vector. The simultaneous confidence regions by LRB can provide insights into estimation uncertainty. Second, using LRB, model confidence bounds (MCB) is constructed to evaluate selection uncertainty. Rigorous proofs establish the consistency properties of the LRB and coverage properties of the MCB. To faciliate implementation, modified local residual bootstrap (mLRB) is proposed, and two visualization curves are introduced to facilitate the assessment and comparison of selection uncertainty. Simulations demonstrate the proposed approaches' practical utility and superiority over closely related alternatives. In the analysis of two real data sets, the proposed analysis provides valuable insights into the uncertainty of the selection results.
