Spectral Analysis of Large Dimensional Random Matrices, 2nd edn

By Cedric E. Ginestet. 2012

285 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a880c51d77a4dba00655d2cc96ec5e1430e5f85e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistical and Nonlinear Physics

Citations in the corpus

Large Dynamic Covariance Matrices (2019, unknown): “This equation has been around for half a century in some form or other, and all researchers in the field are fully confident that “it does exactly what it says on the tin”, even though it is difficult to provide intuitive insight; see Marčenko and Pastur (1967), Silverstein and Bai (1995), Silverste”
Universality and the circular law for sparse random matrices. (2010, background): “This step, in general, follows Krishnapur [34], Appendix C, who investigates a universality principle for nonsparse random matrices with not necessarily i.i.d. entries, since there Dozier and Silverstein’s result [7] cannot be applied.”
Nonparametric eigenvalue-regularized precision or covariance matrix estimator (2016, background): “Theorem 4.1 of Bai and Silverstein (2010) tells us then both Fp and F1p converges to the same limit almost surely under the assumptions (A1) to (A4).”
Limiting laws for divergent spiked eigenvalues and largest nonspiked eigenvalue of sample covariance matrices (2017, background): “10 of [7], we conclude that E|τk|(2) = E| 1 n2 xTkΣ̃1ZkÂ −1 k Z T kΣ̃1xk − 1 n2 trΣ̃1ZkÂ −1 k Z T kΣ̃1| 2 (7.”
On the Marčenko-Pastur law for linear time series (2013, methodology): “One may refer to Anderson et al. [2], Bai and Silverstein [5] and Tao [34] to study various aspects of this literature.”
Universality for the largest eigenvalue of sample covariance matrices with general population (2013, background): “One can refer to [3] or [1] for detailed discussions.”
Optimal estimation of a large-dimensional covariance matrix under Stein’s loss (2018, unknown): “The domain of mtn,p is the strict upper half of the complex plane, but it can be extended to the real line, since Silverstein and Choi [39] prove that ∀λ ∈ R, limz∈C+→λ mtn,p(z) =: m̆tn,p(λ) exists.”
Independence test for high dimensional data based on regularized canonical correlation coefficients (2015, background): “5) recovers [19]’s result (one may refer to the result of F matrix in [5]).”