LARGE SAMPLE COVARIANCE MATRICES WITHOUT INDEPENDENCE STRUCTURES IN COLUMNS

By Z. Bai, Wang Zhou. 2008

188 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2cbb74b146b9263d8ca05952087ba3d3d85581a8

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Citations in the corpus

Capturing the learning curves of generic features maps for realistic data sets with a teacher-student model (2021, background): “While this is still restrictive, stronger results can be shown, and [59, 61, 76, 47] extended them (also loosening the independence assumption) for a very generic class of distributions of correlated random vectors u.”
On the limiting spectral distribution for a large class of symmetric random matrices with correlated entries (2015, background): “Bai and Zhou [3], Yao [18], Banna and Merlevède [4] and Merlevède and Peligrad [14], among others, treated large covariance matrices based on an independent structure between columns and correlated random variables in rows.”
Optimal Shrinkage-Based Portfolio Selection in High Dimensions (2016, background): “Although this assumption looks quite restrictive for financial applications, there exist stronger results from random matrix theory which show that the model can be extended to (weakly) depending variables by demanding more complicated conditions on the elements of Yn (see, Bai and Zhou (2008)) or b”
Random matrix theory in statistics: A review (2014, methodology): “Significant relaxations on the conditions of Theorem 3.4 have been made by Bai and Zhou (2008) who dealt with matrices of the form n 1YnYnn where the columns of the p n matrix Yn are independent but there may be arbitrary dependence within each column.”
Tracy-Widom law for the extreme eigenvalues of sample correlation matrices (2011, unknown): “The asymptotic property of Fp was studied in [11] and [2].”
A note on a Marčenko–Pastur type theorem for time series (2011, background): “1 of Bai and Zhou (2008), it holds that the ESD of npSn converges almost surely to a nonrandom probability distribution whose Stieltjes transform m solves the equation z = − 1 m + 1 c ∫ x 1 +mx dH(x) = − 1 m + 1 2πc ∫ 2π”
Testing Cross-Sectional Correlation in Large Panel Data Models with Serial Correlation (2016, background): “Bai and Zhou [20] use this representation and show that 1/Ttr(Σκ) is bounded for any fixed positive integer κ.”