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This talk is on the problem of testing linear hypotheses in a multivariate regression model with a high-dimensional response and spiked noise covariance. The proposed family of tests consists of test statistics based on weighted sums of projections of the data onto the estimated latent factor directions, with the weights acting as 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 between volumetric measurements of human brain and behavioral variables. The talk is based on joint work with Haoran Li, Debashis Paul and Jie Peng.
Short Bio: Alexander Aue is a professor in the Department of Statistics at the University of California, Davis. He holds a BS degree in Mathematics from Philipps University Marburg and a PhD degree in Applied Mathematics from the University of Cologne, both in Germany. His primary research expertise is in time series, in particular for functional and high–dimensional models. Aue was elected a Fellow of the American Statistical Association in 2016 and of the Institute of Mathematical Statistics in 2018. He is also the 2016 recipient of the UC Davis Chancellor's Award for Excellence in Mentoring Undergraduate Research. Aue is a co-editor of the Journal of Time Series Analysis and serves as an associate editor for a number of leading statistics journals, including the Annals of Statistics. He is the Program Director of the interdisciplinary major in Data Science housed in the Department of Statistics at UC Davis.
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