Online Program Home
My Program

Abstract Details

Activity Number: 547 - Annals of Statistics Special Invited Session: Selected Papers
Type: Invited
Date/Time: Wednesday, July 31, 2019 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #300068
Title: Testing in High-Dimensional Spiked Models
Author(s): Iain Johnstone* and Alexei Onatski
Companies: Stanford University and Cambridge University
Keywords: principal components; canonical correlation; equality of covariance; random matrix theory; wishart matrix

We consider the five classes of multivariate statistical problems identified by James (1964), which together cover much of classical multivariate analysis, plus a simpler limiting case, symmetric matrix denoising. Each of James' problems involves the eigenvalues of E^{-1}H where H and E are proportional to high dimensional Wishart matrices. Under the null hypothesis, both Wisharts are central with identity covariance. Under the alternative, the non-centrality or the covariance parameter of H has a single eigenvalue, a spike, that stands alone. When the spike is smaller than a case-specific phase transition threshold, none of the sample eigenvalues separate from the bulk, making the testing problem challenging. Using a unified strategy for the six cases, we show that the log likelihood ratio processes parameterized by the value of the sub-critical spike converge to Gaussian processes with logarithmic correlation. We then derive asymptotic power envelopes for tests for the presence of a spike.

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

Back to the full JSM 2019 program