【主讲人简介】：Xiucai Ding is currently an associate professor of statistics at UC Davis. Previously, he was a postdoc in Duke. He obtained his PhD from the University of Toronto. His main research interest includes applied probability methods (random matrix theory, random graph theory and Riemann-Hilbert approach) to high dimensional statistics, manifold learning and deep learning theory, as well as nonstationary time series analysis.

【内容简介】：Inference for edge eigenvalues of large covariance matrices is a basic problem in high-dimensional statistics, with important applications to spike detection and principal component analysis. A central difficulty is that the native edge fluctuation occurs at the Tracy-Widom scale n^{-2/3}, with a model-dependent normalization that is often difficult to estimate in practice. In this talk, I will present a multiplier bootstrap approach that deliberately regularizes the edge fluctuation to a slightly larger scale, of order n^{-2/3+\epsilon}, where Gaussian approximation becomes tractable. The method is based on a calibrated family of feasible multipliers and a recentering step that corrects the systematic shift induced by the bootstrap perturbation. This leads to a practical procedure for confidence intervals and testing at the spectral edge. I will discuss the main construction, the role of universality in motivating the calibration step, and the theoretical intuition behind why a slightly enlarged fluctuation scale can lead to more stable inference. Numerical experiments show that the resulting procedure performs accurately in finite samples.

【讲座时间】：2026年7月2日（星期四）上午10:30

【讲座地点】：人文社科科研楼1801会议室