Rank 1 real Wishart spiked model
By M. Y. Mo. 2011
56 citations recorded by the source corpus.
In this paper, we consider N‐dimensional real Wishart matrices Y in the class \input amssym $W_{\Bbb R} (\Sigma ,M)$ in which all but one eigenvalue of Σ is 1. Let the nontrivial eigenvalue of Σ be 1+τ; then as N, M → ∞, with M/N → γ2 finite and nonzero, the eigenvalue distribution of Y will converge into the Marchenko‐Pastur distribution inside a bulk region. When τ increases from 0, one starts to see a stray eigenvalue of Y outside of the support of the Marchenko‐Pastur density. As this stray eigenvalue leaves the bulk region, a phase transition will occur in the largest eigenvalue distribution of the Wishart matrix.
Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/991011c93fc8341d8ffacac1d1bae7764498fcc9
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In Discrete Mathematics and Combinatorics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Asymptotic power of sphericity tests for high-dimensional data (2013, methodology): “This uniformity is a consequence of Lemma A2 proven in the Supplementary Appendix [Onatski, Moreira and Hallin (2013)].”
- Tracy-Widom Distribution for the Largest Eigenvalue of Real Sample Covariance Matrices with General Population (2014, background): “The equivalent of the above mentioned phase transition were obtained in the real setting in [7, 8, 29, 23].”
- Limits of spiked random matrices I (2010, methodology): “Since this article was first posted, Mo [40] gave a different treatment of the real rank one case.”
- Universality for the largest eigenvalue of sample covariance matrices with general population (2013, background): “On the spiked Wishart models, one can refer to [4] for the standard complex case and [9, 10, 34, 41, 55] for the real case.”