CONVERGENCE RATE OF EXPECTED SPECTRAL DISTRIBUTIONS OF LARGE RANDOM MATRICES PART II: SAMPLE COVARIANCE MATRICES

Zhidong Bai

Type: Article

Publication Date: 2008-02-01

Citations: 1

DOI: https://doi.org/10.1142/9789812793096_0011

Abstract

Advances in Statistics, pp. 84-107 (2008) No AccessCONVERGENCE RATE OF EXPECTED SPECTRAL DISTRIBUTIONS OF LARGE RANDOM MATRICES PART II: SAMPLE COVARIANCE MATRICESZ. D. BAIZ. D. BAIDepartment of Statistics, 341 Speakman Hall, Temple University, Philadelphia, Pennsylvania 19122, USAhttps://doi.org/10.1142/9789812793096_0011Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: In the first part of the paper, we developed certain inequalities to bound the difference between distributions in terms of their Stieltjes transforms and established a convergence rate of expected spectral distributions of large Wigner matrices. The second part is devoted to establishing convergence rates for the sample covariance matrices, for the cases where the ratio of the dimension to the degrees of freedom is bounded away from 1 or close to 1, respectively. Keywords: Berry–Essen inequalityconvergence ratelarge dimensional random matrixMarchenko–Pastur distributionsample covariance matrixsemicircular lawspectral analysisStieltjes transformWigner matrixAMSC: 60F15, 62F15 FiguresReferencesRelatedDetails Advances in StatisticsMetrics History KeywordsBerry–Essen inequalityconvergence ratelarge dimensional random matrixMarchenko–Pastur distributionsample covariance matrixsemicircular lawspectral analysisStieltjes transformWigner matrixPDF download

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