Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 129, Issue -, Pages 69-81Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2014.04.002
Keywords
Random matrix theory; Characteristic roots; Largest eigenvalue; Tracy-Widom distribution; Wishart matrices; Gaussian Orthogonal Ensemble
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Funding
- Italian Ministry of Education, Universities and Research (MIUR) under the PRIN Research Project GRETA
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We derive efficient recursive formulas giving the exact distribution of the largest eigenvalue for finite dimensional real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the limiting distribution of large random matrices, we also found that the Tracy-Widom law can be approximated by a properly scaled and shifted gamma distribution, with great accuracy for the values of common interest in statistical applications. (C) 2014 Elsevier Inc. All rights reserved.
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