Event Date
Speaker: Nina Dörnemann (Post-Doctoral Scholar, Statistics, Ruhr-Universität Bochum, Germany; visiting UC Davis)
Title: "Linear spectral statistics of sequential sample covariance matrices"
Abstract: In this talk, we revisit the investigation of linear eigenvalue statistics of sample covariance matrices in high dimensions. Such statistics are frequently used to construct tests for various hypotheses on large covariance matrices. In the meanwhile classical work of Bai and Silverstein (2004), the authors establish a central limit theorem for the linear spectral statistics of sample covariance matrices, which has been generalized in various follow-up works.
In contrast to previous results, we will take a different point of view on linear spectral statistics and study these objects from a sequential perspective. More precisely, we will introduce the sequential sample covariance matrix, which admits a process of eigenvalue statistics. Our interest in such objects is partially motivated by change-point problems in statistics. In our work, we establish the weak convergence of this process of spectral statistics towards a non-standard Gaussian process.
In the final part of this talk, we will discuss a procedure to monitor the sphericity assumption on high dimensional covariance matrices.
This talk is based on a joint work with Holger Dette.
Seminar Date/Time: Tuesday March 7th, 2023, at 4:10pm
Location: MSB 1147 (Colloquium Room)
Refreshments: 3:30pm, MSB Courtyard