### 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.

Original language | English |
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Title of host publication | Encyclopedia of Environmetrics, 2nd Edition |

Editors | W. Piegorsch, A. El Shaarawi |

Publisher | Wiley |

Pages | 910-915 |

Number of pages | 3510 |

ISBN (Print) | 9780470973882 |

Publication status | Published - 2012 |

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## Cite this

Hallin, M., & Jurechova, J. (2012). Equivariant estimation. In W. Piegorsch, & A. El Shaarawi (Eds.),

*Encyclopedia of Environmetrics, 2nd Edition*(pp. 910-915). Wiley.