Please use this identifier to cite or link to this item:
Title: Asymptotic properties of eigenmatrices of a large sample covariance matrix
Authors: Bai, Z.D.
Liu, H.X. 
Wong, W.K.
Keywords: Central limit theorems
Haar distribution
Linear spectral statistics
Marčenko-Pastur law
Random matrix
Sample covariance matrix
Semicircular law
Issue Date: Oct-2011
Citation: Bai, Z.D., Liu, H.X., Wong, W.K. (2011-10). Asymptotic properties of eigenmatrices of a large sample covariance matrix. Annals of Applied Probability 21 (5) : 1994-2015. ScholarBank@NUS Repository.
Abstract: Let Sn = 1/n XnXn where Xn = {X ij} is a p × n matrix with i.i.d. complex standardized entries having finite fourth moments. Let Yn(t1, t 2,σ)=√p(xn(t1) *(Sn +σI)-1xn(t2)-x n(t1)*xn(t2)m n(σ)) in which σ > 0 and mn(σ)= ∫dFyn(x)/x+σ where Fyn(x) is the Marčenko-Pastur law with parameter yn = p/n; which converges to a positive constant as n → ∞ and xn(t1) and xn(t2) are unit vectors in ℂp, having indices t 1 and t2, ranging in a compact subset of a finite-dimensional Euclidean space. In this paper, we prove that the sequence Yn(t1, t2, σ) converges weakly to a (2m + 1)-dimensional Gaussian process. This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of S n is asymptotically close to that of a Haar-distributed unitary matrix. © 2011 Institute of Mathematical Statistics.
Source Title: Annals of Applied Probability
ISSN: 10505164
DOI: 10.1214/10-AAP748
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.


checked on Oct 17, 2018


checked on Oct 9, 2018

Page view(s)

checked on Aug 16, 2018

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.