Session B5 - Random Matrices
July 13, 15:30 ~ 15:55 - Room B3
Random matrices, M-estimators and the bootstrap
Noureddine El Karoui
UC, Berkeley, USA - firstname.lastname@example.org
Random-matrices-inspired ideas and techniques can be used to understand a wide variety of problems in high-dimensional statistics, way beyond properties of correlation and covariance matrices. In this talk, I'll discuss how RMT is a fundamental tool in understanding the properties of widely used methods such as M-estimators and the bootstrap in high-dimensional statistics. Interestingly, the corresponding analyses upend conventional statistical thinking: maximum likelihood methods are woefully inefficient (even among restricted classes of estimators) and the bootstrap typically fails to give statistically valid confidence statements, even for very simple problems. I'll also discuss limitations of random matrix models for statistical applications.
Joint work with Elizabeth Purdom (UC, Berkeley).