Robustness and efficiency properties of scatter matrices

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The robustness and efficiency properties of likelihood ratio tests for functions of the population covariance matrix are studied. An alternative class of tests based upon affine-invariant M-estimates of scatter is proposed whenever the function of the covariance matrix is invariant under a common scale change. For such inferences, it is shown that a single scalar-valued index of efficiency is sufficient.

Original languageEnglish (US)
Pages (from-to)411-420
Number of pages10
Issue number2
StatePublished - Aug 1 1983
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • Affine-invariant M-estimate
  • Asymptotic distribution
  • Covariance matrix
  • Elliptical distribution
  • Likelihood ratio test
  • Maximum likelihood test
  • Multivariate t

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