The Tracy–Widom limit for the largest eigenvalues of singular complex Wishart matrices
By A. Onatski. 2008
74 citations recorded by the source corpus.
This paper extends the work of El Karoui [Ann. Probab. 35 (2007) 663--714] which finds the Tracy--Widom limit for the largest eigenvalue of a nonsingular $p$-dimensional complex Wishart matrix $W_{\mathbb{C}}(\Omega_p,n)$ to the case of several of the largest eigenvalues of the possibly singular $(n<p)$ matrix $W_{\mathbb{C}}(\Omega_p,n).$ As a byproduct, we extend all results of Baik, Ben Arous and Peche [Ann. Probab. 33 (2005) 1643--1697] to the singular Wishart matrix case. We apply our findings to obtain a 95% confidence set for the number of common risk factors in excess stock returns.
Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/f8beb4b01cbf66fd74bd5ab448fd345e24537df1
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Citations in the corpus
- Universality for the largest eigenvalue of sample covariance matrices with general population (2013, methodology): “1 below will be employed, whereby El Karoui showed in [12] that the TW2 limit holds for the standard complex nonnull Wishart matrices when d > 1 (nonsingular case), followed by Onatski’s extension to the singular case (0 < d ≤ 1) in [38].”
- TESTING HYPOTHESES ABOUT THE NUMBER OF FACTORS IN LARGE FACTOR MODELS (2009, methodology): “inequality limsupl1ncm,n Onatski (2007) , which we rely on in our”
- A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices (2016, background): “ satisfy arbitrary sub-expoenetial distribution [29, 30]. When T is a (non-scalar) diagonal matrix, the Tracy-Widom distribution was proved for Wishart matrix X first in [11] (non-singular T case) and [27] (singular T case). Later the edge universality for diagonal T was proved in [6, 23] for all ran”
- Rank 1 real Wishart spiked model (2011, result): “This has led to the results in [10] and results on the largest eigenvalue distributions for more general complex Wishart ensembles [38], [57].”
- DYNAMIC FACTOR MODELS (2018, methodology): “Onatski (2008) extends El Karoui (2007) to provide a joint limit (a vector Tracy-Widom law) for the centered and rescaled first several eigenvalues.”
- Anisotropic local laws for random matrices (2014, methodology): “22) originally appeared in [9] and has been used in many subsequent works [4, 21, 24] on the distribution of eigenvalues near the rightmost edge.”
- Tracy-Widom Distribution for the Largest Eigenvalue of Real Sample Covariance Matrices with General Population (2014, background): “3) in the sub-critical regime were given in [12] for the non-singular case d ∈ (0,∞), d 6= 1, and [32] for the singular case d = 1.”
- Spiked separable covariance matrices and principal components (2019, background): “ly distributed entries was proved later in [48]. When Aris a general non-scalar matrix, the Tracy-Widom distribution for the extremal eigenvalues was first proved for the case with i.i.d.Gaussian X in [17, 40]; the edge universality was later proved under various moment assumptions on the entries xij”