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Title: Testing general linear hypotheses under a high-dimensional spiked model Authors:  Debashis Paul - University of California, Davis (United States) [presenting]
Abstract: The problem of testing linear hypotheses associated with a high dimensional multivariate linear regression model is considered when the noise covariance has a spiked covariance structure. The classical test for this kind of hypotheses based on the likelihood ratio statistic suffers from substantial loss of power when the dimensionality of the observations is comparable to the sample size. To mitigate this problem, we propose a class of regularized test procedures that rely on a nonlinear shrinkage of the eigenvalues and eigen-projections of the sample noise covariance matrix, under the assumption that the population noise covariance matrix has a spiked covariance structure. We solve the problem of finding the optimal regularization parameter through a probabilistic formulation of the alternatives. We compare the performance of the proposed test with several tests proposed in the literature through numerical studies.