On the cumulants of affine equivariant estimators in elliptical families

Rudolf Grübel, David M Rocke

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

Given a statistical model for data which take values in Rd and have elliptically distributed errors, and affine equivariant estimators μ̂ and μ̂ of a mean vector in Rd⊗Rn and a d × d scatter matrix, expressions are given for the covarances of the estimators in terms of their expectations and some unknown constants that depend on the model and the estimator. Higher order cumulants are also developed. These results place considerable constraints on the possible cumulants of μ̂ and μ̂, as wel as those of estimators of higher order behavior such as multivariate skewness and kurtosis. These expressions are obtained using tensor methods.

Original languageEnglish (US)
Pages (from-to)203-222
Number of pages20
JournalJournal of Multivariate Analysis
Volume35
Issue number2
DOIs
StatePublished - 1990

Keywords

  • maximum likelihood
  • multivariate location
  • multivariate regression
  • robust estimation
  • seemingly unrelated regression
  • tensor methods

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Numerical Analysis
  • Statistics and Probability

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