An overview of large-dimensional covariance and precision matrix estimators with applications in chemometrics

Jasper Engel*, Lutgarde Buydens, Lionel Blanchet

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Web of Science)

Abstract

The covariance matrix (or its inverse, the precision matrix) is central to many chemometric techniques. Traditional sample estimators perform poorly for high-dimensional data such as metabolomics data. Because of this, many traditional inference techniques break down or produce unreliable results. In this paper, we selectively review several modern estimators of the covariance and precision matrix that improve upon the traditional sample estimator. We focus on 3 general techniques: eigenvalue-shrinkage estimation, ridge-type estimation, and structured estimation. These methods rely on different assumptions regarding the structure of the covariance or precision matrix. Various examples, in particular using metabolomics data, are used to compare these techniques and to demonstrate that in concert with, eg, principal component analysis, multivariate analysis of variance, and Gaussian graphical models, better results are obtained.

We selectively review modern estimators of the covariance and precision matrix focusing on 3 general techniques, namely, eigenvalue-shrinkage estimation, ridge-type estimation, and structured estimation. These methods rely on different structural assumptions of the covariance or precision matrix. Various examples, in particular using metabolomics data, are used to compare these techniques and to demonstrate that in concert with, eg, principal component analysis, multivariate analysis of variance, and Gaussian graphical models, better results are obtained.

Original languageEnglish
Article numbere2880
Number of pages19
JournalJournal of Chemometrics
Volume31
Issue number4
DOIs
Publication statusPublished - Apr 2017

Keywords

  • eigenvalue shrinkage
  • metabolomics
  • ridge-type estimation
  • sparse covariance matrix
  • sparse precision matrix
  • TOTAL CORRELATION SPECTROSCOPY
  • PENALIZED NORMAL LIKELIHOOD
  • NUCLEAR-MAGNETIC-RESONANCE
  • GAUSSIAN GRAPHICAL MODELS
  • SHRINKAGE ESTIMATION
  • METABOLOMICS DATA
  • SPARSE ESTIMATION
  • LASSO
  • SELECTION
  • INVERSE

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