Some Connections Between Random Matrices and Statistics

• Activity Number: 106
• Type: Invited
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Statistical Learning and Data Mining Section
• Author(s): Noureddine El Karoui*+
• Companies: UC Berkeley
• Keywords: random matrices ; high-dimensional statistics

Abstract

With data collection and storage easier by the day, statisticians are now working with datasets having many observations and many measurements per observations. This is a radical shift from the classical theory of statistics, where the number of observations (n) is most often assumed to be much bigger than the number of measurements per observations (p). It is therefore important to understand how statistical estimators behave and perform in the setting where both p and n are large. Because random matrices are a key building block of statistics, the theory of high-dimensional random matrices is helpful in shedding light on certain high-dimensional (i.e large p, large n) statistical problems. In this talk, I will discuss some of these problems, as well as potential limitations of the standard models of random matrix theory when used in a statistical setting.