Measuring the influence of the kth largest variable on functions over the unit hypercube

Marichal, Jean-Luc; Mathonet, Pierre

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 : Mathematics Business & 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
Name of the research project :	F1R-MTH-PUL-09MRDO > MRDO > 01/01/2009 - 31/12/2011 > MARICHAL Jean-Luc
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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