CLT for linear spectral statistics of large-dimensional sample covariance matrices

By Zhidong Bai, J. Silverstein. 2008

501 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/14dc92e649a9339e3290f65973cbc6ad9d84f69a

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Citations in the corpus

On asymptotics of eigenvectors of large sample covariance matrix (2007, methodology): “It follows, via (4.3) of [ 7 ] and the assumption of Theorem 2, that”
Corrections to LRT on large-dimensional covariance matrix by RMT (2009, methodology): “Proofs Proof of (3.3) By Theorem 2.1, for g(x) = x− log x− 1, by using the variable change x = 1 + y − 2√y cos θ, 0 ≤ θ ≤ π, we have m(g) = g (a(y)) + g (b(y)) 4 − 1 2π ∫ b(y) a(y) g(x)√ 4y − (x − 1 − y)2 dx = y − log(1 − y) 2 − 1 2π ∫ π 0 [1 + y − 2√y cos θ − log(1 + y − 2√y cos θ) − 1] dθ = y − lo”
On the distribution of SINR for the MMSE MIMO receiver and performance analysis (2006, methodology): “We use some known results for the empirical eigenvalue distribution (ESD) of the product of two random matrices (e.g, Silverstein [20], Bai [21], Silverstein and Bai [ 22 ]), to study the asymptotic properties of T . We work under the regime:”
Fluctuations of the Extreme Eigenvalues of Finite Rank Deformations of Random Matrices (2010, unknown): “Moreover, by [3, Th. 1.1] or [4, Th. 9.10], we also know that a central limit theorem holds for the linear statistics of Wishart matrices, giving Hypothesis 3.1 as in the Wigner case.”
ASYMPTOTICS OF SAMPLE EIGENSTRUCTURE FOR A LARGE DIMENSIONAL SPIKED COVARIANCE MODEL (2007, background): “Bai and Silverstein (2004) derived the asymptotic distribution of certain linear spectral statistics.”
CENTRAL LIMIT THEOREM FOR LINEAR EIGENVALUE STATISTICS OF RANDOM MATRICES WITH INDEPENDENT ENTRIES (2008, background): “For real analytic test functions this formula is a particular case of the variance, obtained in [5] for random matrices n−1X∗TX , where X is a complex matrix with i.”
High dimensional correlation matrices: the central limit theorem and its applications (2017, methodology): “Bai and Silverstein (2004) contributed to the establishment of asymptotic theory for LSSs based on high dimensional sample covariance matrices.”
The Dynamics of Learning: A Random Matrix Approach (2018, methodology): “We follow the idea in (Bai & Silverstein, 2008) and choose the contour γb to be a rectangle with sides parallel to the axes, intersecting the real axis at 0 and λ+ (in fact at −ǫ and λ+ + ǫ so that the functions under consideration remain analytic) and the horizontal sides being a distance ε → 0…”
On estimation of the noise variance in high dimensional probabilistic principal component analysis (2013, background): “F cn;Hn ](dx), f2A, where Ais the set of analytic functions f : U!C, with Uan open set of C such that [1 (0;1)(c)a(c);b(c)] ˆU. We will need the following CLT which is a combination of Theorem 1.1 of Bai and Silverstein (2004) and a recent addition proposed in Zheng et al. (2014). Proposition 1. We ”
ON ESTIMATION OF THE POPULATION SPECTRAL DISTRIBUTION FROM A HIGH‐DIMENSIONAL SAMPLE COVARIANCE MATRIX (2010, methodology): “We first use a CLT for linear statistics provided in Bai and Silverstein [1](Theorem 1.”
Fluctuations of eigenvalues of random normal matrices (2008, background): “Results related to fluctuations of eigenvalues of Hermitian matrices, are found in Johansson [26] and also [3], [4] and [21].”
A CLT FOR INFORMATION-THEORETIC STATISTICS OF GRAM RANDOM MATRICES WITH A GIVEN VARIANCE PROFILE (2007, unknown): “Although phrased differently, such a centering procedure relying on a deterministic equivalent is used in [1] and [3].”
GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES (2012, background): “, [3]) to calculate central limit theorems for generalized Wishart matrices; for a good reference on the methodology involved, we recommend [4].”
On the sphericity test with large-dimensional observations (2013, methodology): “the Marčenko-Pastur distribution F y (y < 1) in [2], F (log x) = y − 1 y log(1− y)− 1, F (x) = 1.”