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Title: High dimensional hypothesis testing via spectral shrinkage Authors:  Haoran Li - Columbia University (United States) [presenting]
Alexander Aue - UC Davis (United States)
Debashis Paul - University of California, Davis (United States)
Abstract: Inference on high-dimensional data has remained a central topic of statistical research for over a decade. One of the fundamental inferential problems is to test a linear hypothesis under linear models. Under high-dimensional regimes, mainly due to the inconsistency of classical matrix estimators, such as the sample covariance matrix, traditional inferential procedures, such as the likelihood ratio tests (LRT), perform poorly. To correct the inconsistency of LRT, we propose a flexible spectral shrinkage scheme applied to the sample covariance matrix. The spectral shrinkage adjusts the singularity or near-singularity of the sample covariance matrix and meanwhile maintains its eigen-structure. The scheme is shown to compare favorably against a host of existing methods designed to tackle high-dimensional testing problems in a wide range of settings.