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Equivariant Estimation

Statistical Theory and Methods

  1. Marc Hallin1,2,
  2. Jana JureČková3

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vnn082

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Hallin, M. and JureČková, J. 2013. Equivariant Estimation. Encyclopedia of Environmetrics. 2.

Author Information

  1. 1

    ECARES, Université libre de Bruxelles, Bruxelles, Belgium

  2. 2

    Princeton University, Princeton, NJ, USA

  3. 3

    Charles University, Prague, Czech Republic

Publication History

  1. Published Online: 15 JAN 2013

Abstract

The concepts of invariance and equivariance of estimators with respect to various groups of transformations of the sample space are defined. The structure and properties of equivariant and minimum risk equivariant estimators are characterized. Emphasis is put on equivariance with respect to shift, scale, and affine transformations.

Keywords:

  • invariance;
  • equivariance;
  • risk;
  • Pitman estimator;
  • multivariate model;
  • affine-equivariance;
  • admissibility;
  • Mahalanobis distance