Eigenvalue estimation of parameterized covariance matrices of large dimensional data

Jianfeng Yao*, Abla Kammoun, Jamal Najim

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

This article deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although such a regime is of interest for many current statistical signal processing and wireless communication issues, traditional methods fail to produce consistent estimators and only recently results relying on large random matrix theory have been unveiled. In this paper, we develop the parametric framework proposed by Mestre, and consider a model where the covariance matrix to be estimated has a (known) finite number of eigenvalues, each of it with an unknown multiplicity. The main contributions of this work are essentially threefold with respect to existing results, and in particular to Mestre's work: To relax the (restrictive) separability assumption, to provide joint consistent estimates for the eigenvalues and their multiplicities, and to study the variance error by means of a Central Limit Theorem.

Original languageEnglish (US)
Article number6262495
Pages (from-to)5893-5905
Number of pages13
JournalIEEE Transactions on Signal Processing
Volume60
Issue number11
DOIs
StatePublished - Oct 22 2012

Keywords

  • Central limit theorem
  • Stieltjes transform
  • covariance matrix estimation
  • moment method
  • random matrix theory

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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