The limiting distributions of eigenvalues of sample correlation matrices

By Tiefeng Jiang. 2004

91 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/06b10b3d7204595b9e7eac995a8e5883bf4bfdf1

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Citations in the corpus

Testing Cross-Sectional Correlation in Large Panel Data Models with Serial Correlation (2016, methodology): “As shown in the Random Matrix Theory (RMT) literature, the sample covariance 29 and correlation matrices are ill-conditioned since their eigenvectors are not consistent to their 30 population counterparts, see Johnstone [20] and Jiang [19].”
Edge universality of correlation matrices (2011, background): “in result, and more importantly, we do not need this result in our proof (see Remark 1.3). The almost sure convergence of the largest and smallest eigenvalues of correlation matrix was established in [14]. The very recent paper [1], relying on our results in [21], shows that the asymptotic distribut”
Random matrix theory in statistics: A review (2014, methodology): “They used this result to prove that the ESD of a sample correlation matrix converges almost surely to the Marčenko–Pastur law, thus extending the scope of a result by Jiang (2004).”
High dimensional correlation matrices: the central limit theorem and its applications (2017, background): “Moreover, the estimators are consistent according to theorem 2 of Jiang (2004) or the proof of this paper.”
Tracy-Widom law for the extreme eigenvalues of sample correlation matrices (2011, methodology): “on, the eigenvalues of W will be denoted by 0 ≤ λ 1 ≤ λ 2 ≤ ··· ≤ λp. Then the empirical distribution (ESD) of W is deﬁned by Fp(x) = 1 p Xp i=1 1{λ i≤x}. The asymptotic property of Fp was studied in [11] and [2]. For the almost sure convergence of λ 1 and λp, see [11]. In this paper, we will study ”
LARGE SAMPLE COVARIANCE MATRICES WITHOUT INDEPENDENCE STRUCTURES IN COLUMNS (2008, unknown): “Spectral distributions of sample correlation matrices were first studied by Jiang (2004) under second moment conditions.”
Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles (2006, background): “Recently, Jiang (2004) proved that the largest and the smallest eigenvalue converge a.”
Econometric Analysis of Vast Covariance Matrices Using Composite Realized Kernels and Their Application to Portfolio Choice (2016, background): “This area of study is called "random matrix theory" and surveys of the main idea and the literatures are given by Johnstone (2001) and Johnstone (2010) and a survey in the context of finance is given in Gatheral (2008) and Bouchaud & Potters (2011).”
Concentration of measure and spectra of random matrices: Applications to correlation matrices, elliptical distributions and beyond (2009, methodology): “However, [27] required only four moments and we require a little more.”