CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size

CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size

Let A = 1/√np(XT X−pIn) where X is a p×n matrix, consisting of independent and identically distributed (i.i.d.) real random variables Xij with mean zero and variance one. When p/n→∞, under fourth moment conditions a central limit theorem (CLT) for linear spectral statistics (LSS) of A defined by the...

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Bibliographic Details
Main Authors: Chen, Binbin, Pan, Guangming
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2015
Subjects:
DRNTU::Science::Physics::Atomic physics
Online Access:https://hdl.handle.net/10356/107446
http://hdl.handle.net/10220/25620
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Institution: Nanyang Technological University
Language: English
Description
Summary:Let A = 1/√np(XT X−pIn) where X is a p×n matrix, consisting of independent and identically distributed (i.i.d.) real random variables Xij with mean zero and variance one. When p/n→∞, under fourth moment conditions a central limit theorem (CLT) for linear spectral statistics (LSS) of A defined by the eigenvalues is established. We also explore its applications in testing whether a population covariance matrix is an identity matrix.

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