Probability & Statistics Day, 2013

University of California, San Diego, Friday, April 5th, 2013

Iain Johnstone (Stanford University)

Random matrices in statistics: testing in spiked models

Principal components analysis is a staple of multivariate statistical analysis. Viewed as the study of the eigenvalues of a sample covariance matrix, it is an important example for random matrix theory. The talk will explore the interplay between these two subjects by focusing on covariance matrices which are drawn from low rank perturbations of a scaled identity matrix. Such models arise in settings as diverse as finance, genetics and signal processing -- brief examples will be given. We give an overview of some results of several people on estimating and testing in settings with both weak and strong signals.

 

Iain Johnstone is Marjorie Mhoon Fair Professor in Quantitative Science in the Department of Statistics at Stanford University. He holds a joint appointment in Biostatistics in Stanford’s School of Medicine. He received his Ph.D. in Statistics from Cornell in 1981. His research has used ideas from harmonic analysis, such as wavelets, to understand noise-reduction methods in signal and image processing. More recently, he has applied random matrix theory to the study of high-dimensional multivariate statistical methods, such as principal components and canonical correlation analysis. A native of Australia, Johnstone is a member of the U.S. National Academy of Sciences and the American Academy of Arts and Sciences and a former president of the Institute of Mathematical Statistics.