Reference : Measuring the influence of the kth largest variable on functions over the unit hypercube
 Document type : Scientific congresses, symposiums and conference proceedings : Paper published in a book Discipline(s) : Physical, chemical, mathematical & earth Sciences : MathematicsBusiness & economic sciences : Quantitative methods in economics & management To cite this reference: http://hdl.handle.net/10993/7259
 Title : Measuring the influence of the kth largest variable on functions over the unit hypercube Language : English Author, co-author : Marichal, Jean-Luc [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Mathonet, Pierre [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit] Publication date : 19-Oct-2010 Main document title : Modeling Decisions for Artificial Intelligence: Proceedings 7th International Conference, MDAI 2010, Perpignan, France, October 27-29, 2010 Editor : Torra, Vicenc Narukawa, Yasuo Daumas, Marc Publisher : Springer-Verlag Collection and collection volume : Lecture Notes in Artificial Intelligence Vol. 6408 Pages : 7-18 Peer reviewed : Yes On invitation : No Audience : International ISBN : 978-3-642-16291-6 City : Berlin Country : Germany Event name : 7th Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI 2010) Event date : from 27-10-2010 to 29-10-2010 Event organizer : Vicenc Torra (IIIA-CSIC, South Catalonia, Spain) Yasuo Narukawa (Toho Gakuen, Japan) Event place (city) : Perpignan Event country : France Abstract : [en] By considering a least squares approximation of a given square integrable function $f\colon [0,1]^n\to\R$ by a shifted $L$-statistic function (a shifted linear combination of order statistics), we define an index which measures the global influence of the $k$th largest variable on $f$. We show that this influence index has appealing properties and we interpret it as an average value of the difference quotient of $f$ in the direction of the $k$th largest variable or, under certain natural conditions on $f$, as an average value of the derivative of $f$ in the direction of the $k$th largest variable. We also discuss a few applications of this index in statistics and aggregation theory. Funders : University of Luxembourg - UL Target : Researchers ; Professionals ; Students Permalink : http://hdl.handle.net/10993/7259 Other URL : http://www.mdai.cat/mdai2010/ http://www.springer.com/computer/ai/book/978-3-642-16291-6

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