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This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form $\mathcal{W}_N=\Sigma^{1/2}XX^*\Sigma ^{1/2}$.
Lindeberg, J. W.J. W. (1922). Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung. Math. Z. 15 211–225
1922
Earlier work this paper cites.
Fisher, R. A.R. A. (1939). The sampling distribution of some statistics obtained from non-linear equations. Ann. Eugenics 9 238–249
1939
Earlier work this paper cites.
Hsu, P. L.P. L. (1939). On the distribution of roots of certain determinantal equations. Ann. Eugenics 9 250–258
1939
Earlier work this paper cites.
Roy, S. N.S. N. (1939). p-Statistics and some generalizations in analysis of variance appropriate to multivariate problems. Sankhyā 4 381–396
1939
Earlier work this paper cites.
Marčenko, V. A.V. A. andPastur, L. A.L. A. (1967). Distribution for some sets of random matrices. Math. USSR-Sb. 1 457–483
1967
Earlier work this paper cites.
Eaton, Morris L.M. L. (1989). Group Invariance Applications in Statistics. NSF-CBMS Regional Conference Series in Probability and Statistics 1. IMS, Hayward, CA
1989
Earlier work this paper cites.
Tracy, Craig A.C. A. andWidom, HaroldH. (1994). Level-spacing distributions and the Airy kernel. Comm. Math. Phys. 159 151–174
1994
Earlier work this paper cites.
Silverstein, Jack W.J. W. andChoi, Sang-IlS.-I. (1995). Analysis of the limiting spectral distribution of large-dimensional random matrices. J. Multivariate Anal. 54 295–309
1995
Earlier work this paper cites.
Tracy, Craig A.C. A. andWidom, HaroldH. (1996). On orthogonal and symplectic matrix ensembles. Comm. Math. Phys. 177 727–754
1996
Earlier work this paper cites.
Kay, S. M.S. M. (1998). Fundamentals of Statistical Signal Processing, Vol. II: Detection Theory. Prentice Hall, Upper Saddle River, NJ
1998
Earlier work this paper cites.
Bai, Z. D.Z. D. (1999). Methodologies in spectral analysis of large-dimensional random matrices, a review. Statist. Sinica 9 611–677
1999
Earlier work this paper cites.
Johansson, KurtK. (2000). Shape fluctuations and random matrices. Comm. Math. Phys. 209 437–476
2000
Earlier work this paper cites.
Johnstone, Iain M.I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 295–327
2001
Earlier work this paper cites.
Soshnikov, AlexanderA. (2002). A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices. J. Stat. Phys. 108 1033–1056
2002
Earlier work this paper cites.
Baik, JinhoJ., Ben Arous, GérardG. andPéché, SandrineS. (2005). Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33 1643–1697
2005
Earlier work this paper cites.
2006
Earlier work this paper cites.
El Karoui, NoureddineN. (2007). Tracy–Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices. Ann. Probab. 35 663–714
2007
Earlier work this paper cites.
Johnstone, Iain M.I. M. (2007). High dimensional statistical inference and random matrices. In International Congress of Mathematicians I 307–333. Eur. Math. Soc., Zürich
2007
Earlier work this paper cites.
Onatski, A.A. (2007). A formal statistical test for the number of factors in the approximate factor models. Unpublished manuscript
2007
Earlier work this paper cites.
Paul, DebashisD. (2007). Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statist. Sinica 17 1617–1642
2007
Earlier work this paper cites.
Bai, ZhidongZ. andYao, Jian-fengJ.-f. (2008). Central limit theorems for eigenvalues in a spiked population model. Ann. Inst. Henri Poincaré Probab. Stat. 44 447–474
2008
Cited alongside, same era.
Nadakuditi, Raj RaoR. R. andEdelman, AlanA. (2008). Sample eigenvalue based detection of high-dimensional signals in white noise using relatively few samples. IEEE Trans. Signal Process. 56 2625–2638
2008
Cited alongside, same era.
Onatski, AlexeiA. (2008). The Tracy–Widom limit for the largest eigenvalues of singular complex Wishart matrices. Ann. Appl. Probab. 18 470–490
2008
Cited alongside, same era.
El Karoui, NoureddineN. (2009). Concentration of measure and spectra of random matrices: Applications to correlation matrices, elliptical distributions and beyond. Ann. Appl. Probab. 19 2362–2405
2009
Cited alongside, same era.
Tao, TerenceT. andVu, VanV. (2011). Random matrices: Universality of local eigenvalue statistics. Acta Math. 206 127–204
2011
Later among the works it cites.
Bao, ZhigangZ., Pan, GuangmingG. andZhou, WangW. (2012). Tracy–Widom law for the extreme eigenvalues of sample correlation matrices. Electron. J. Probab. 17 1–32
2012
Later among the works it cites.
Erdős, LászlóL., Knowles, AnttiA., Yau, Horng-TzerH.-T. andYin, JunJ. (2012). Spectral statistics of Erdös–Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Comm. Math. Phys. 314 587–640
2012
Later among the works it cites.
Erdős, LászlóL., Schlein, BenjaminB., Yau, Horng-TzerH.-T. andYin, JunJ. (2012). The local relaxation flow approach to universality of the local statistics for random matrices. Ann. Inst. Henri Poincaré Probab. Stat. 48 1–46
2012
Later among the works it cites.
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Erdős, LászlóL., Schlein, BenjaminB. andYau, Horng-TzerH.-T. (2009). Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices. Ann. Probab. 37 815–852
2009
Cited alongside, same era.
Erdős, LászlóL., Schlein, BenjaminB. andYau, Horng-TzerH.-T. (2009). Local semicircle law and complete delocalization for Wigner random matrices. Comm. Math. Phys. 287 641–655
2009
Cited alongside, same era.
Féral, DelphineD. andPéché, SandrineS. (2009). The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case. J. Math. Phys. 50 073302
2009
Cited alongside, same era.
Onatski, AlexeiA. (2009). Testing hypotheses about the numbers of factors in large factor models. Econometrica 77 1447–1479
2009
Cited alongside, same era.
Paul, DebashisD. andSilverstein, Jack W.J. W. (2009). No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix. J. Multivariate Anal. 100 37–57
2009
Cited alongside, same era.
Péché, SandrineS. (2009). Universality results for the largest eigenvalues of some sample covariance matrix ensembles. Probab. Theory Related Fields 143 481–516
2009
Cited alongside, same era.
2009
Cited alongside, same era.
Bai, ZhidongZ. andSilverstein, Jack W.J. W. (2010). Spectral Analysis of Large Dimensional Random Matrices, 2nd ed. Springer, New York
2010
Cited alongside, same era.
Erdős, LászlóL., Yau, Horng-TzerH.-T. andYin, JunJ. (2012). Bulk universality for generalized Wigner matrices. Probab. Theory Related Fields 154 341–407
2012
Later among the works it cites.
Erdős, LászlóL., Yau, Horng-TzerH.-T. andYin, JunJ. (2012). Rigidity of eigenvalues of generalized Wigner matrices. Adv. Math. 229 1435–1515
2012
Later among the works it cites.
Mo, M. Y.M. Y. (2012). Rank 1 real Wishart spiked model. Comm. Pure Appl. Math. 65 1528–1638
2012
Later among the works it cites.
Pillai, Natesh S.N. S. andYin, JunJ. (2012). Edge universality of correlation matrices. Ann. Statist. 40 1737–1763
2012
Later among the works it cites.
Tao, TerenceT. andVu, VanV. (2012). Random covariance matrices: Universality of local statistics of eigenvalues. Ann. Probab. 40 1285–1315
2012
Later among the works it cites.
Wang, DongD. (2012). The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, Part I. J. Stat. Phys. 146 719–761
2012
Later among the works it cites.
Wang, KeK. (2012). Random covariance matrices: Universality of local statistics of eigenvalues up to the edge. Random Matrices Theory Appl. 1 1150005, 24
2012
Later among the works it cites.
Bao, Z. G.Z. G., Pan, G. M.G. M. andZhou, W.W. (2013). Local density of the spectrum on the edge for sample covariance matrices with general population. Preprint
2013
Closest in time.
Bloemendal, AlexA. andVirág, BálintB. (2013). Limits of spiked random matrices I. Probab. Theory Related Fields 156 795–825
2013
Closest in time.
Onatski, AlexeiA., Moreira, Marcelo J.M. J. andHallin, MarcM. (2013). Asymptotic power of sphericity tests for high-dimensional data. Ann. Statist. 41 1204–1231
2013
Closest in time.
Vinogradova, JuliaJ., Couillet, RomainR. andHachem, WalidW. (2013). Statistical inference in large antenna arrays under unknown noise pattern. IEEE Trans. Signal Process. 61 5633–5645
2013
Closest in time.
Bao, ZhigangZ., Pan, GuangmingG. andZhou, WangW. (2014). Supplement to “Universality for the largest eigenvalue of sample covariance matrices with general population.” DOI: \doiurl
2014
Closest in time.
Lee, Ji OonJ. O. andYin, JunJ. (2014). A necessary and sufficient condition for edge universality of Wigner matrices. Duke Math. J. 163 117–173
2014
Closest in time.
Pillai, Natesh S.N. S. andYin, JunJ. (2014). Universality of covariance matrices. Ann. Appl. Probab. 24 935–1001
2014
Closest in time.
Wang, LiliL. andPaul, DebashisD. (2014). Limiting spectral distribution of renormalized separable sample covariance matrices when p / n → 0 p/n\to 0 . J. Multivariate Anal. 126 25–52
2014
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