Paper published in a book (Scientific congresses, symposiums and conference proceedings)
Measuring the influence of the kth largest variable on functions over the unit hypercube
Marichal, Jean-Luc; Mathonet, Pierre
2010 • In Torra, Vicenc; Narukawa, Yasuo; Daumas, Marc (Eds.) Modeling Decisions for Artificial Intelligence: Proceedings 7th International Conference, MDAI 2010, Perpignan, France, October 27-29, 2010
[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.
Disciplines :
Mathematics Quantitative methods in economics & management
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
Language :
English
Title :
Measuring the influence of the kth largest variable on functions over the unit hypercube
Publication date :
19 October 2010
Event name :
7th Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI 2010)