A measure of mutual complete dependence
| dc.contributor.author | Siburg, Karl Friedrich | |
| dc.contributor.author | Stoimenov, Pavel A. | |
| dc.date.accessioned | 2007-05-25T12:33:09Z | |
| dc.date.available | 2007-05-25T12:33:09Z | |
| dc.date.issued | 2007-05-25T12:33:09Z | |
| dc.description.abstract | Two 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 Lp-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 approx- imate 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. AMS 2000 subject classifcations: Primary 62E10; secondary 62H20 | en |
| dc.identifier.uri | http://hdl.handle.net/2003/24317 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-14804 | |
| dc.language.iso | en | de |
| dc.subject | Copulas | en |
| dc.subject | Mutual complete dependence | en |
| dc.subject | Nonparametric measures of dependence | en |
| dc.subject | Sobolev norm | en |
| dc.subject.ddc | 004 | |
| dc.title | A measure of mutual complete dependence | en |
| dc.type | Text | de |
| dc.type.publicationtype | report | en |
| dcterms.accessRights | open access |