Equivariant estimation

M. Hallin, J. Jurechova

    Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

    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 languageEnglish
    Title of host publicationEncyclopedia of Environmetrics, 2nd Edition
    EditorsW. Piegorsch, A. El Shaarawi
    PublisherWiley
    Pages910-915
    Number of pages3510
    ISBN (Print)9780470973882
    Publication statusPublished - 2012

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    Equivariance
    Equivariant
    Equivariant Estimator
    Sample space
    Affine transformation
    Invariance
    Estimator
    Concepts

    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.
    Hallin, M. ; Jurechova, J. / Equivariant estimation. Encyclopedia of Environmetrics, 2nd Edition. editor / W. Piegorsch ; A. El Shaarawi. Wiley, 2012. pp. 910-915
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    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.",
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    note = "Pagination: 3510",
    year = "2012",
    language = "English",
    isbn = "9780470973882",
    pages = "910--915",
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    booktitle = "Encyclopedia of Environmetrics, 2nd Edition",
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    Hallin, M & Jurechova, J 2012, Equivariant estimation. in W Piegorsch & A El Shaarawi (eds), Encyclopedia of Environmetrics, 2nd Edition. Wiley, pp. 910-915.

    Equivariant estimation. / Hallin, M.; Jurechova, J.

    Encyclopedia of Environmetrics, 2nd Edition. ed. / W. Piegorsch; A. El Shaarawi. Wiley, 2012. p. 910-915.

    Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

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    AB - 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.

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    BT - Encyclopedia of Environmetrics, 2nd Edition

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    A2 - El Shaarawi, A.

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    Hallin M, Jurechova J. Equivariant estimation. In Piegorsch W, El Shaarawi A, editors, Encyclopedia of Environmetrics, 2nd Edition. Wiley. 2012. p. 910-915