| Title:
|
Exact distribution under independence of the diagonal section of the empirical copula (English) |
| Author:
|
Erdely, Arturo |
| Author:
|
González–Barrios, José M. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
44 |
| Issue:
|
6 |
| Year:
|
2008 |
| Pages:
|
826-845 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we analyze some properties of the empirical diagonal and we obtain its exact distribution under independence for the two and three- dimensional cases, but the ideas proposed in this paper can be carried out to higher dimensions. The results obtained are useful in designing a nonparametric test for independence, and therefore giving solution to an open problem proposed by Alsina, Frank and Schweizer [2]. (English) |
| Keyword:
|
Archimedean copula |
| Keyword:
|
diagonal section |
| Keyword:
|
independence |
| MSC:
|
60C05 |
| MSC:
|
62E15 |
| MSC:
|
62H05 |
| idZBL:
|
Zbl 1252.60015 |
| idMR:
|
MR2488910 |
| . |
| Date available:
|
2009-09-24T20:40:42Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135894 |
| . |
| Reference:
|
[1] Aguiló I., Suñer, J., Torrens J.: Matrix representation of discrete quasi-copulas.Fuzzy Sets and Systems 159 (2008), 1658–1672 MR 2419976, 10.1016/j.fss.2007.10.004 |
| Reference:
|
[2] Alsina C., Frank M. J., Schweizer B.: Associative Functions: Triangular Norms and Copulas.World Scientific Publishing Co., Singapore 2006 Zbl 1100.39023, MR 2222258 |
| Reference:
|
[3] Bailey D. F.: Counting arrangements of 1’s and $-1$’s.Math. Mag. 69 (1996), 128–131 Zbl 0859.05007, MR 1573156 |
| Reference:
|
[4] Barcucci E., Verri M. C.: Some more properties of Catalan numbers.Discrete Math. 102 (1992), 229–237 Zbl 0757.05005, MR 1169143, 10.1016/0012-365X(92)90117-X |
| Reference:
|
[5] Callan D.: Some bijections and identities for the Catalan and Fine numbers.Séminaire Lotharingen de Combinatoire 53 (2006), B53e (16 pp) Zbl 1084.05002, MR 2221363 |
| Reference:
|
[6] Cameron N. T.: Random Walks, Trees and Extensions of Riordan Group Techniques.Ph.D. Thesis. Howard University 2002 MR 2703896 |
| Reference:
|
[7] Chung K. L., Feller W.: On fluctuations in coin-tossing.Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 605–608 MR 0033459, 10.1073/pnas.35.10.605 |
| Reference:
|
[8] Darsow W. F., Frank M. J.: Associative functions and Abel–Schröder systems.Publ. Math. Debrecen 30 (1983), 253–272 Zbl 0542.39001, MR 0739487 |
| Reference:
|
[9] Deheuvels P.: La fonction de dépendance empirique et ses propriétés.Un test non paramétrique d’indépendance. Acad. Roy. Belg. Bull. Cl. Sci. 65 (1979), 5, 274–292 Zbl 0422.62037, MR 0573609 |
| Reference:
|
[10] Engleberg E. O.: On some problems concerning a restricted random walk.J. Appl. Probab. 2 (1965), 396–404 MR 0182993, 10.2307/3212201 |
| Reference:
|
[11] Erdely A.: Diagonal Properties of the Empirical Copula and Applications.Construction of Families of Copulas with Given Restrictions. Ph.D. Thesis, Universidad Nacional Autónoma de México 2007 |
| Reference:
|
[12] Feller W.: An Introduction to Probability Theory and Its Applications, Vol.1. Third edition. Wiley, New York 1968 Zbl 0598.60003, MR 0228020 |
| Reference:
|
[13] Frank M. J.: Diagonals of copulas and Schröder’s equation.Aequationes Math. 51 (1996), 150 MR 1144584 |
| Reference:
|
[14] Kimberling C. H.: A probabilistic interpretation of complete monotonicity.Aequationes Math. 10 (1974), 152–164 Zbl 0309.60012, MR 0353416, 10.1007/BF01832852 |
| Reference:
|
[15] Klement E. P., Mesiar, R., Pap E.: Triangular Norms.Kluwer Academic Publishers, Dordrecht 2000 Zbl 1087.20041, MR 1790096 |
| Reference:
|
[16] Klement E. P., Mesiar R.: Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms.Elsevier, Amsterdam 2005 Zbl 1063.03003, MR 2166082 |
| Reference:
|
[17] Kolesárová A., Mesiar R., Mordelová, J., Sempi C.: Discrete Copulas.IEEE Trans. Fuzzy Systems 14 (2006), 698–705 10.1109/TFUZZ.2006.880003 |
| Reference:
|
[18] Kolesárová A., Mordelová J.: Quasi-copulas and copulas on a discrete scale.Soft Computing 10 (2006), 495–501 Zbl 1096.60012, 10.1007/s00500-005-0524-6 |
| Reference:
|
[19] Kuczma M.: Functional Equations in a Single Variable.Polish Scientific Publishers, Warsaw 1968 Zbl 0725.39003, MR 0228862 |
| Reference:
|
[20] Kuczma M., Choczewski, B., Ger R.: Iterative Functional Equations.Cambridge University Press, New York 1990 Zbl 1141.39023, MR 1067720 |
| Reference:
|
[21] Mayor G., Suner, J., Torrens J.: Copula-like operations on finite settings.IEEE Trans. Fuzzy Systems 13 (2005), 468–477 10.1109/TFUZZ.2004.840129 |
| Reference:
|
[22] McNeil A. J., Nešlehová J.: Multivariate Archimedean copulas, $D$-monotone functions and $l_{1}$-norm symmetric distributions.Ann. Statist, to appear MR 2541455 |
| Reference:
|
[23] Mesiar R.: Discrete copulas – what they are.In: Joint EUSFLAT-LFA 2005, Conference Proc. (E. Montsenyand P. Sobrevilla, eds.) Universitat Politecnica de Catalunya, Barcelona 2005, pp. 927–930 |
| Reference:
|
[24] Nelsen R. B.: An Introduction to Copulas.Second edition. Springer, New York 2006 Zbl 1152.62030, MR 2197664 |
| Reference:
|
[25] Schweizer B., Sklar A.: Probabilistic Metric Spaces.North-Holland, New York 1983 Zbl 0546.60010, MR 0790314 |
| Reference:
|
[26] Sklar A.: Fonctions de répartition à $n$ dimensions et leurs marges.Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 MR 0125600 |
| Reference:
|
[27] Sungur E. A., Yang Y.: Diagonal copulas of Archimedean class.Comm. Statist. Theory Methods 25 (1996), 1659–1676 Zbl 0900.62339, MR 1411104, 10.1080/03610929608831791 |
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