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Title: Tracy-Widom law of ridge-regularized F-matrix and applications Authors:  Haoran Li - Auburn University (United States) [presenting]
Abstract: In Multivariate Data Analysis, many central problems can be formulated as a double Wishart problem where two Wishart matrices, $W_1$ and $W_2$, are involved. Important cases include MANOVA, CCA, and tests for linear hypotheses in multivariate linear regression. The traditional Roy's largest root test relies on the largest eigenvalue of the F-matrix $F=W_1W_2^{-1}$. In a high-dimensional setting, the test is infeasible due to the singularity of $W_2$. To fix the singularity, we propose a ridge-regularized test where a ridge term is added to $W_2$. We derive the asymptotic Tracy-Widom distribution of the largest eigenvalue of the regularized F-matrix. Efficient methods for estimating the asymptotic mean and variance are designed through the Marchenko-Pastur equation. The power characteristics are studied under a class of local alternatives. A simulation study is carried out to examine the numerical performance of the proposed tests.