A seminar by Professor Alexander Aue from University of California Davis
Title: Testing general linear hypotheses under a high-dimensional multivariate regression model with spiked noise covariance
Abstract: We consider the problem of testing linear hypotheses under a multivariate re- gression model with a high dimensional response and spiked noise covariance. The proposed family of tests consists of test statistics based on a weighted sum of pro- jections of the data onto the estimated latent factor directions, with the weights acting as the regularization parameters. We establish asymptotic normality of the test statistics under the null hypothesis. We also establish the power characteristics of the tests and propose a data-driven choice of the regularization parameters under
a family of local alternatives. The performance of the proposed tests is evaluated through a simulation study. Finally, the proposed tests are applied to the Human Connectome Project data to test for the presence of associations.
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