Integral trimmed regions
AbstractWe define a new family of central regions with respect to a probability measure. They are induced by a set or a family of sets of functions and we name them integral trimmed regions. The halfspace trimming and the zonoid trimming are particular cases of integral trimmed regions. We focus our work on the derivation of properties of such integral trimmed regions from conditions satisfied by the generating classes of functions. Further we show that, under mild conditions, the population integral trimmed region of a given depth can be characterized in terms of certain regions based on empirical distributions.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 96 (2005)
Issue (Month): 2 (October)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Fernández, Ignacio Cascos & Molchanov, Ilya, 2003. "A stochastic order for random vectors and random sets based on the Aumann expectation," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 295-305, July.
- Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008.
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Working Papers ECARES
2008_042, ULB -- Universite Libre de Bruxelles.
- Marc Hallin & Davy Paindaveine & Miroslav Šiman, 2010. "Multivariate quantiles and multiple-output regression quantiles: From L1 optimization to halfspace depth," ULB Institutional Repository 2013/127979, ULB -- Universite Libre de Bruxelles.
- Ignacio Cascos, 2006. "The Expected Convex Hull Trimmed Regions Of A Sample," Statistics and Econometrics Working Papers ws066919, Universidad Carlos III, Departamento de Estadística y Econometría.
- Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate risks and depth-trimmed regions," Papers math/0606520, arXiv.org, revised Nov 2006.
- 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.
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