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Activity Number:
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506
- Advances in Multivariate Analysis for High-Dimensional, Complex Data Problems
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Type:
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Topic Contributed
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Date/Time:
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Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
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Sponsor:
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Korean International Statistical Society
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Abstract #328558
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Presentation
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Title:
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Computing Conditional Density of Eigenvalues in High-Dimension
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Author(s):
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Yunjin Choi*
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Companies:
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National University of Singapore
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Keywords:
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Random matrix;
Eigenvalue distribution;
Principal component
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Abstract:
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We propose a method 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. Johnstone (2001) addressed this issue 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.
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Authors who are presenting talks have a * after their name.
