Title:
|
A subcopula based dependence measure (English) |
Author:
|
Erdely, Arturo |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 (print) |
ISSN:
|
1805-949X (online) |
Volume:
|
53 |
Issue:
|
2 |
Year:
|
2017 |
Pages:
|
231-243 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the proposed dependence measure based on the empirical subcopula is provided, along with an R package to perform the corresponding calculations. (English) |
Keyword:
|
subcopula |
Keyword:
|
dependence |
Keyword:
|
concordance |
MSC:
|
62H20 |
idZBL:
|
Zbl 06770166 |
idMR:
|
MR3661350 |
DOI:
|
10.14736/kyb-2017-2-0231 |
. |
Date available:
|
2017-06-25T17:55:31Z |
Last updated:
|
2018-01-10 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146803 |
. |
Reference:
|
[1] Cifarelli, D. M., Conti, P. L., Regazzini, E.: On the asymptotic distribution of a general measure of monotone dependence..Ann. Statist. 24 (1996), 1386-1399. Zbl 0862.62014, MR 1401856, 10.1214/aos/1032526975 |
Reference:
|
[2] Denuit, M., Lambert, P.: Constraints on concordance measures in bivariate discrete data..J. Mult. Anal. 93 (2005), 40-57. Zbl 1095.62065, MR 2119763, 10.1016/j.jmva.2004.01.004 |
Reference:
|
[3] Durante, F., Sempi, C.: Principles of Copula Theory..CRC Press, Boca Raton 2016. MR 3443023, 10.1201/b18674 |
Reference:
|
[4] Erdely, A.: subcopem2D: Bivariate Empirical Copula..R package version 1.2 (2017), URL |
Reference:
|
[5] Genest, C., Nešlehová, J.: A primer on copulas for count data..Astin Bull. 37 (2007), 475-515. Zbl 1274.62398, MR 2422797, 10.2143/ast.37.2.2024077 |
Reference:
|
[6] Genest, C., Nešlehová, J., Rémillard, B.: On the empirical multilinear copula process for count data..Bernoulli 20 (2014), 1344-1371. MR 3217446, 10.3150/13-bej524 |
Reference:
|
[7] Hofert, M., Kojadinovic, I., Maechler, M., Yan, J.: copula: Multivariate Dependence with Copulas..R package version 0.999-16 (2017), URL |
Reference:
|
[8] Lehmann, E. L.: Some concepts of dependence..Ann. Math. Statist. 37 (1966), 1137-1153. Zbl 0146.40601, MR 0202228, 10.1214/aoms/1177699260 |
Reference:
|
[9] Li, X., Mikusiński, P., Sherwood, H., Taylor, M. D: On approximation of copulas..In: Distributions with given marginals and moment problems (V. Beneš and J. Štěpán, eds.), Kluwer, Dordrecht 1997, pp. 107-116. Zbl 0905.60015, MR 1614663, 10.1007/978-94-011-5532-8_13 |
Reference:
|
[10] Nelsen, R. B.: An Introduction to Copulas..Springer, New York 2006. Zbl 1152.62030, MR 2197664, 10.1007/0-387-28678-0 |
Reference:
|
[11] Nešlehová, J.: On rank correlation measures for non-continuous random variables..J. Mult. Anal. 98 (2007), 544-567. Zbl 1107.62047, MR 2293014, 10.1016/j.jmva.2005.11.007 |
Reference:
|
[12] Team, R Core: R: A language and environment for statistical computing..R Foundation for Statistical Computing (Vienna), URL |
Reference:
|
[13] Scarsini, M.: On measures of concordance..Stochastica 8 (1984), 201-218. Zbl 0582.62047, MR 0796650 |
Reference:
|
[14] Schweizer, B., Wolff, E. F.: On nonparametric measures of dependence for random variables..Ann. Statist. 9 (1981), 879-885. Zbl 0468.62012, MR 0619291, 10.1214/aos/1176345528 |
Reference:
|
[15] Sklar, A.: Fonctions de répartition à $n$ dimensions et leurs marges..Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231. MR 0125600 |
. |