Pre-Synposis
Speaker: Mayukh Choudhury, IIT Bombay
Host: Debraj Das
Title: Asymptotic Theory of Bootstrap in Generalized Linear Models
Time, day and date: 4:00:00 PM – 5:00:00 PM, Friday, February 27
Venue: Ramanujan Hall
Abstract: Generalized Linear Models (GLMs) are central to modern statistical analysis, but classical inference methods often become challenging in the presence of regularization, high dimensionality, and data-driven model selection. This talk develops a unified theoretical framework for Bootstrap-based inference in GLMs addressing structurally regularized models, addressing challenges arising from sparsity, growing dimensionality, cross validated tuning, and low-rank constraints. The first part establishes the validity of Bootstrap methods for Lasso estimators in generalized linear models, where traditional asymptotic approximations fail due to penalization bias. The second part develops high-dimensional distributional approximations of the GLM estimator based on Bootstrap when the dimension may grow exponentially with sample size. The third part provides rigorous asymptotic analysis of usual Lasso estimators tuned via K-fold cross-validation, clarifying the inferential impact of data-dependent penalty selection. The final part extends the theory developed in the first part to the matrix linear model setting. In this part, a valid Bootstrap method is developed for low-rank parameter matrix estimation under nuclear-norm penalization. Together, these results provide theoretical foundations and practical tools for reliable inference in modern high-dimensional statistical models.