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The Expected Convex Hull Trimmed Regions Of A Sample

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  • Ignacio Cascos

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    Abstract

    Given a data set in the multivariate Euclidean space, we study regions of central points built by averaging all their subsets with a fixed number of elements. The averaging of these sets is performed by appropriately scaling the Minkowski or elementwise summation of their convex hulls. The volume of such central regions is proposed as a multivariate scatter estimate and a circular sequence algorithm to compute the central regions of a bivariate data set is described.

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    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws066919.

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    Date of creation: Dec 2006
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    Handle: RePEc:cte:wsrepe:ws066919

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    1. Elyés Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued coherent risk measures," Finance and Stochastics, Springer, vol. 8(4), pages 531-552, November.
    2. Cascos, Ignacio & López-Díaz, Miguel, 2005. "Integral trimmed regions," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 404-424, October.
    3. Ruts, Ida & Rousseeuw, Peter J., 1996. "Computing depth contours of bivariate point clouds," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 153-168, November.
    4. Masse, J. C. & Theodorescu, R., 1994. "Halfplane Trimming for Bivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 48(2), pages 188-202, February.
    5. K. Mosler, 2003. "Central regions and dependency," Econometrics 0309004, EconWPA.
    6. Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate Risks And Depth-Trimmed Regions," Statistics and Econometrics Working Papers ws063815, Universidad Carlos III, Departamento de Estadística y Econometría.
    7. Touzi, Nizar & Meddeb, Moncef & Jouini, Elyès, 2004. "Vector-valued Coherent Risk Measures," Economics Papers from University Paris Dauphine 123456789/353, Paris Dauphine University.
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