Full metadata record
DC FieldValueLanguage
dc.contributor.authorSiburg, Karl F.-
dc.contributor.authorStoimenov, Pavel A.-
dc.date.accessioned2008-05-15T10:33:30Z-
dc.date.available2008-05-15T10:33:30Z-
dc.date.issued2008-05-15T10:33:30Z-
dc.identifier.urihttp://hdl.handle.net/2003/25271-
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-15871-
dc.description.abstractTwo random variables X and Y are mutually completely dependent (m.c.d.) if there is a measurable bijection f with P(Y = f(X)) = 1. For continuous X and Y , a natural approach to constructing a measure of dependence is via the distance between the copula of X and Y and the independence copula. We show that this approach depends crucially on the choice of the distance function. For example, the L^p-distances, suggested by Schweizer and Wolff, cannot generate a measure of (mutual complete) dependence, since every copula is the uniform limit of copulas linking m.c.d. variables. Instead, we propose to use a modified Sobolev norm, with respect to which, mutual complete dependence cannot approximate any other kind of dependence. This Sobolev norm yields the first nonparametric measure of dependence capturing precisely the two extremes of dependence, i.e., it equals 0 if and only if X and Y are independent, and 1 if and only if X and Y are m.c.d.en
dc.language.isoende
dc.relation.ispartofseriesPreprints der Fakultät für Mathematik;2008-08de
dc.subjectMeasure of dependenceen
dc.subjectMutual complete dependenceen
dc.subjectCopulaen
dc.subjectSobolev normen
dc.subject.ddc510-
dc.titleA measure of mutual complete dependenceen
dc.typeTextde
dc.type.publicationtypepreprinten
dcterms.accessRightsopen access-
Appears in Collections:Preprints der Fakultät für Mathematik

Files in This Item:
File Description SizeFormat 
mathematicalPreprint08.pdf323.45 kBAdobe PDFView/Open


This item is protected by original copyright



This item is protected by original copyright rightsstatements.org