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Title: Testing high-dimensional general linear hypotheses under a multivariate regression model with spiked noise covariance Authors:  Haoran Li - Columbia University (United States)
Alexander Aue - UC Davis (United States) [presenting]
Debashis Paul - University of California, Davis (United States)
Jie Peng - University of California Davis (United States)
Abstract: The problem of testing linear hypotheses under a high-dimensional multivariate regression model with spiked noise covariance is considered. The proposed family of tests consists of test statistics based on a weighted sum of projections of the data onto the factor directions, with the weights acting as the regularization parameters. We establish the asymptotic normality of the proposed family of test statistics under the null hypothesis. We also establish the power characteristics of the tests under a family of probabilistic local alternatives and derive the minimax choice of the regularization parameters. The performance of the proposed tests is evaluated in comparison with several competing tests. Finally, the proposed tests are applied to the Human Connectome Project data to test for the presence of an association between volumetric measurements of the human brain and certain behavioral variables.