Large covariance matrix estimation: Bridging shrinkage and tapering approaches

Xiaohui Chen, Z. Jane Wang, Martin J. McKeown

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we propose a shrinkage-to-tapering oracle (STO) estimator for estimation of large covariance matrix when the number of samples is substantially fewer than the number of variables, by combining the strength from both Steinian-type shrinkage and tapering estimators. Our contributions include: (i) Deriving the Frobenius risk and a lower bound for the spectral risk of an MMSE shrinkage estimator; (ii) Deriving a closed-form expression for the optimal coefficient of the proposed STO estimator. Simulations on auto-regression (e.g. a sparse case) and fraction Brownian motion (e.g. a non-sparse case) covariance structures are used to demonstrate the superiority of the proposed estimator.

Original languageEnglish (US)
Title of host publication2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings
Pages2013-2016
Number of pages4
DOIs
StatePublished - Oct 23 2012
Externally publishedYes
Event2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Kyoto, Japan
Duration: Mar 25 2012Mar 30 2012

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012
CountryJapan
CityKyoto
Period3/25/123/30/12

Keywords

  • Covariance matrix
  • high-dimensionality
  • shrinkage estimator
  • tapering estimator

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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