Bootstrapping Linear and Non-Linear Spectral Statistics in High Dimensions

Statistics arising from the eigenvalues of sample covariance matrices, known as spectral statistics, are fundamental to many tasks in high-dimensional inference. In particular, the problem of approximating the distributions of spectral statistics is often a key issue in constructing hypothesis tests and confidence intervals. Commonly, this problem is addressed using asymptotic formulas based on random matrix theory. However, such formulas are specialized to particular types of spectral statistics, and entail other practical difficulties. In recent years, progress has been made toward showing that bootstrap methods can provide accurate distributional approximations while also being easier to apply to a wider range of statistics. In this talk, I will give an overview of my past and ongoing research on this topic. (Joint work from projects with Alexander Aue, Andrew Blandino, Nina Doernemann, and Siyao Wang.)

About Miles Lopes

Miles Lopes is Associate Professor of Statistics at UC Davis. He received B.S. degrees in mathematics and physics from UCLA, as well as an M.S. in computer science and a Ph.D. in statistics from UC Berkeley, where he was advised by Peter Bickel. His main areas of research are high-dimensional inference and error analysis of randomized algorithms, with an emphasis on bootstrap methods.