Stay Informed:

COVID-19 (coronavirus) information
Zoom Links: Zoom Help | Teaching with Zoom | Zoom Quick Guide

STAT Seminar Series: Tests for high-dimensional general linear hypotheses through spectral shrinkage

Speaker Name: 
Debashis Paul
Speaker Title: 
Speaker Organization: 
UC Davis
Start Time: 
Monday, May 13, 2019 - 4:00pm
End Time: 
Monday, May 13, 2019 - 5:00pm

Title: Tests for high-dimensional general linear hypotheses through spectral shrinkage

Abstract: We consider the problem of testing linear hypotheses associated with a high-dimensional multivariate linear regression model under the setting where the dimensionality of the response is comparable to the sample size. Classical likelihood ratio tests for such problems suffer from significant loss of power within this asymptotic framework. We propose regularization schemes that modify the likelihood ratio statistic by applying nonlinear shrinkage to the eigenvalues of the empirical covariance matrix of the regression residuals. We propose two different classes of regularized tests to deal with two different types of structural assumptions on the covariance matrix of the noise: (a) the spectral measure of the noise covariance converges to a nontrivial limit; and (b) the noise covariance has a spiked covariance structure.  We show that in each case, the proposed tests are able to significantly improve on the performance of the likelihood ratio test. We address the problem of finding the optimal regularization parameter within a decision-theoretic framework by adopting a probabilistic formulation of the alternatives. 


(This is a joint work with Haoran Li, Alexander Aue and Jie Peng).