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Title: Computing conditional density of eigenvalues in high-dimension Authors:  Yunjin Choi - National University of Singapore (Singapore) [presenting]
Abstract: A method is proposed for evaluating conditional density of eigenvalues of a Wishart matrix in high-dimension. Evaluating the density of eigenvalues involve multi-dimensional integration, while multi-dimensional integration can be computationally challenging especially in high-dimensional setting. This issue has been previously addressed by utilizing approximation of a random matrix kernel and proposed a method for evaluating the marginal distribution of the largest eigenvalue of a Wishart matrix. We extend this approach and propose a method for evaluating the conditional distribution of any $k$-th eigenvalue with its preceding eigenvalues conditioned. The proposed method can be used for testing the significance of the principal components.