Robust estimators for nondecomposable elliptical graphical models

D. Vogel*, D. E. Tyler

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Robust estimators of the restricted covariance matrices associated with elliptical graphical models are studied. General asymptotic results, which apply to both decomposable and nondecomposable graphical models, are presented for robust plug-in type estimators. These extend results previously established only for the decomposable case. Furthermore, a class of graphical M-estimators for the restricted covariance matrices is introduced and compared with the corresponding plug-in M-estimators. The two approaches are shown to be asymptotically equivalent under random sampling from an elliptical distribution. A simulation study demonstrates the superiority of the graphical M-estimators for small samples.

Original languageEnglish
Pages (from-to)865-882
Number of pages18
JournalBiometrika
Volume101
Issue number4
Early online date17 Oct 2014
DOIs
Publication statusPublished - Dec 2014

Keywords

  • affine equivariance
  • deviance test
  • Gaussian graphical model
  • M-estimator
  • partial correlation
  • Maximum-likelihood-estimation
  • maultivariate time-series
  • covariance-matrix
  • asymptotic-behavior
  • Gaussian Models
  • scatter
  • selection
  • location
  • distributions
  • efficiency

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