Spectral analysis of the Moore–Penrose inverse of a large dimensional sample covariance matrix

Taras Bodnar, Holger Dette and Nestor Parolya

Journal of Multivariate Analysis, 2016, vol. 148, issue C, 160-172

Abstract: For a sample of n independent identically distributed p-dimensional centered random vectors with covariance matrix Σn let S̃n denote the usual sample covariance (centered by the mean) and Sn the non-centered sample covariance matrix (i.e. the matrix of second moment estimates), where p>n. In this paper, we provide the limiting spectral distribution and central limit theorem for linear spectral statistics of the Moore–Penrose inverse of Sn and S̃n. We consider the large dimensional asymptotics when the number of variables p→∞ and the sample size n→∞ such that p/n→c∈(1,+∞). We present a Marchenko–Pastur law for both types of matrices, which shows that the limiting spectral distributions for both sample covariance matrices are the same. On the other hand, we demonstrate that the asymptotic distribution of linear spectral statistics of the Moore–Penrose inverse of S̃n differs in the mean from that of Sn.

Keywords: CLT; Large-dimensional asymptotics; Moore–Penrose inverse; Random matrix theory (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X16000646
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:148:y:2016:i:c:p:160-172

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2016.03.001

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().