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Activity Number: 392 - Large-Scale Data Analysis via Spectral Methods
Type: Topic Contributed
Date/Time: Tuesday, July 30, 2019 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #301711
Title: Bootstrapping Spectral Statistics in High Dimensions
Author(s): Miles Lopes* and Alexander Aue and Andrew Blandino
Companies: UC Davis and University of California, Davis and UC Davis
Keywords: bootstrap methods; high-dimensional statistics; covariance matrices; random matrix theory

Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of spectral statistics in low-dimensional problems, these methods are relatively unexplored in the high-dimensional setting. The aim of this paper is to focus on linear spectral statistics as a class of prototypes for developing a new bootstrap in high-dimensions --- and we refer to this method as the Spectral Bootstrap. In essence, the method originates from the parametric bootstrap, and is motivated by the notion that, in high dimensions, it is difficult to obtain a non-parametric approximation to the full data-generating distribution. In addition to proving the consistency of the proposed method, we provide encouraging empirical results in a variety of settings. Lastly, and perhaps most interestingly, we show through simulations that the method can be applied successfully to statistics outside the class of linear spectral statistics, such as the largest sample eigenvalue and others. (Joint work with Alexander Aue and Andrew Blandino.)

Authors who are presenting talks have a * after their name.

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