High-Dimensional Covariance Matrix Estimation by Aygul Zagidullina

High-Dimensional Covariance Matrix Estimation by Aygul Zagidullina

Author:Aygul Zagidullina
Language: eng
Format: epub
ISBN: 9783030800659
Publisher: Springer International Publishing


4.2 Sample Eigenvalues

Under high-dimensional asymptotics, two different cases are considered with regard to the behavior of the sample eigenvalues: the bulk, which refers to the properties of the full set of sample eigenvalues λ n,1, …, λ n,p, and the extremes, which address the largest and smallest eigenvalues.

Moreover, there is a distinction between the null and non-null cases. The null case refers to the situation when the extreme eigenvalues are packed together with the bulk or the majority of the eigenvalues. The non-null case describes the situation when the extreme eigenvalues are separated from the bulk and do not follow the limiting laws that are valid for the null case.



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