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Tail sums of Wishart and Gaussian eigenvalues beyond the bulk edge
Author(s) -
Johnstone Iain M.
Publication year - 2018
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12201
Subject(s) - wishart distribution , mathematics , eigenvalues and eigenvectors , covariance , gaussian , combinatorics , covariance matrix , enhanced data rates for gsm evolution , matrix (chemical analysis) , statistics , multivariate statistics , telecommunications , physics , materials science , quantum mechanics , computer science , composite material
Summary Consider the classical Gaussian unitary ensemble of size N and the real white Wishart ensemble with N variables and n degrees of freedom. In the limits of large N and n , with positive ratio γ in the Wishart case, the expected number of eigenvalues that exit the upper bulk edge is less than one, approaching 0.031 and 0.170 respectively, the latter number being independent of γ . These statements are consequences of quantitative bounds on tail sums of eigenvalues outside the bulk which are established here for applications in high dimensional covariance matrix estimation.