Statistical Estimation and Classification on Commutative Covariance Structures

  • Authors:
  • M. E. Shaikin

  • Affiliations:
  • Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

  • Venue:
  • Automation and Remote Control
  • Year:
  • 2003

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Abstract

Statistical inference is investigated under the following constraints on the covariance structure for the observation vector: covariance matrices belong to some commutative matrix algebra. Commutative approximation of arbitrary covariance structures and statistical estimation of the parameters of a given commutative structure are studied. The results are applied to statistical classification of Gaussian vectors having commutative covariance structure.