Tests of independence and randomness based on the empirical copula process

Test

Volumn 13, Issue 2, 2004, Pages 335-370

  Genest, Christian ^a   Rémillard, Bruno ^b  

^a UNIVERSITÉ LAVAL   (Canada)

^b HEC MONTRÉAL   (Canada)

Author keywords

Copula; Cram r von Mises statistic; Empirical process; M bius inversion formula; Pseudo observations; Semi parametric models; Serial dependence; Tests of independence

Indexed keywords

EID: 13444252724     PISSN: 11330686     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02595777     Document Type: Article

References (40)

1. BARBE, P., GENEST, C., GHOUDI, K., and RÉMILLARD, B. (1996). On Kendall's process. Journal of Multivariate Analysis, 58:197-229.
2. BLUM, J. R., KIEFER, J., and ROSENBLATT, M. (1961). Distribution free tests of independence based on the sample distribution function. The Annals of Mathematical Statistics, 32:485-498.
3. CHATTERJEE, S. and YILMAZ, M. R. (1992). Chaos, fractals and statistics (with discussion). Statistical Science, 7:49-121.
4. CLAYTON, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65:141-151.
5. DEHEUVELS, P. (1979). La fonction de dépendance empirique et ses propriétés: Un test non paramétrique d'indépendance. Académie Royale de Belgique, Bulletin de la Classe des Sciences, 5ième série, 65:274-292.
6. DEHEUVELS, P. (1980). Non parametric tests of independence. In Non-parametric Asymptotic Statistics (Proceedings of the Conference held in Rouen in 1979), pp. 95-107. Lecture Notes in Mathematics No 821, Springer, New York.
7. DEHEUVELS, P. (1981a). An asymptotic decomposition for multivariate distribution-free tests of independence. Journal of Multivariate Analysis, 11:102-113.
8. DEHEUVELS, P. (1981b). A Kolmogorov-Smirnov type test for independence and multivariate samples. Revue Roumaine de Mathématiques Pures et Appliquées, 26:213-226.
9. DEHEUVELS, P. (1981c). A non parametric test for independence. Publications de l'Institut de Statistique de l'Université de Paris, 26:29-50.
10. DELGADO, M. A. (1996). Testing serial independence using the sample distribution function. Journal of Time Series Analysis, 17:271-285.
11. DROUET-MARI, D. and KOTZ, S. (2001). Correlation and Dependence. Imperial College Press, London.
12. DUGUÉ, D. (1975). Sur des tests d'indépendance "indépendants de la loi". Comptes Rendus de l'Académie des Sciences de Paris, Série A, 281:1103-1104.
13. FERGUSON, T. S., GENEST, C., and HALLIN, M. (2000). Kendall's tau for serial dependence. The Canadian Journal of Statistics, 28:587-604.
14. FISHER, R. A. (1950). Statistical Methods for Research Workers, 11th Edition. Oliver and Boyd, London.
15. GÄNSSLER, P. and STUTE, W. (1987). Seminar on Empirical Processes, DMV Seminar 9. Birkhäuser, Basel.
16. GENEST, C. and MACKAY, R. J. (1986). Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données. The Canadian Journal of Statistics, 14:145-159.
17. GENEST, C., QUESSY, J.-F., and RÉMILLARD, B. (2002). Tests of serial independence based on Kendall's process. The Canadian Journal of Statistics, 30:441-461.
18. GHOUDI, K., KULPERGER, R. J., and RÉMILLARD, B. (2001). A nonparametric test of serial independence for time series and residuals. Journal of Multivariate Analysis, 79:191-218.
19. GHOUDI, K. and RÉMILLARD, B. (1998). Empirical processes based on pseudo-observations. In B. Szyszkowicz, ed., Asymptotic Methods in Probability and Statistics: A Volume in Honour of Miklós Csörg″o, pp. 171-197. North-Holland, Amsterdam.
20. GHOUDI, K. and RÉMILLARD, B. (2004). Empirical processes based on pseudo-observations II: The multivariate case. In L. Horváth and B. Szyszkowicz, eds., Asymptotic Methods in Stochastics: Festschrift for Miklós Csörg″o, vol. 44, pp. 381-406. The Fields Institute Communications Series. American Mathematical Society, Providence, RI.
21. GIESER, P. W. and RANDLES, R. H. (1997). A nonparametric test of independence between two vectors. Journal of the American Statistical Association, 92:561-567.
22. GUMBEL, E. J. (1960). Distributions des valeurs extrêmes en plusieurs dimensions. Publications de l'Institut de Statistique de l'Université de Paris, 9:171-173.
23. HALLIN, M., INGENBLEEK, J.-F., and PURI, M. L. (1985). Linear serial rank tests for randomness against ARMA alternatives. The Annals of Statistics, 13:1156-1181.
24. HALLIN, M., INGENBLEEK, J.-F., and PURI, M. L. (1987). Linear and quadratic serial rank tests for randomness against serial dependence. Journal of Time Series Analysis, 8:409-424.
25. HALLIN, M. and PURI, M. L. (1992). Rank tests for time series analysis: A survey. In D. R. Brillinger, E. Parzen, and M. Rosenblatt, eds., New Directions in Time Series Analysis, Part I, pp. 111-153. Springer, New York.
26. HALLIN, M. and WERKER, B. J. M. (1999). Optimal testing for semi-parametric AR models - from Gaussian Lagrange multipliers to autoregression rank scores and adaptive tests. In S. Ghosh, ed., Asymptotics, Nonparametrics, and Time Series, pp. 295-350. Marcel Dekker, New York.
27. HONG, Y. (1998). Testing for pairwise serial independence via the empirical distribution function. Journal of the Royal Statistical Society, Series B, 60:429-453.
28. HONG, Y. (2000). Generalized spectral tests for serial dependence. Journal of the Royal Statistical Society, Series B, 62:557-574.
29. JING, P. and ZHU, L.-X. (1996). Some Blum-Kiefer-Rosenblatt type tests for the joint independence of variables. Communications in Statistics, Theory and Methods, 25:2127-2139.
30. JOE, H. (1997). Multivariate Models and Dependence Concepts. Chapman and Hall, London.
31. KALLENBERG, W. C. M. and LEDWINA, T. (1999). Data-driven rank tests for independence. Journal of the American Statistical Association, 94:285-301.
32. KULPERGER, R. J. and LOCKHART, R. A. (1998). Tests of independence in time series. Journal of Time Series Analysis, 19:165-185.
33. LITTELL, R. C. and FOLKS, J. L. (1973). Asymptotic optimality of Fisher's method of combining independent tests II. Journal of the American Statistical Association, 68:193-194.
34. NELSEN, R. B. (1999). An Introduction to Copulas. Springer, New York.
35. ROMANO, J. P. and SIEGEL, A. F. (1986). Counterexamples in Probability and Statistics. Wadsworth, London.
36. SHIH, J. H. and LOUIS, T. A. (1996). Tests of independence for bivariate survival data. Biometrics, 52:1440-1449.
37. SKAUG, H. J. and TJØSTHEIM, D. (1993). A nonparametric test of serial independence based on the empirical distribution function. Biometrika, 80:591-602.
38. v. In A. Badrijian and P.-L. Hennequin, eds., École d'Été de Probabilités de Saint-Flour III-1973, pp. 115-189. Springer, New York.
39. STUTE, W. (1984). The oscillation behavior of empirical processes: The multivariate case. The Annals of Probability, 12:361-379.
40. TJØSTHEIM, D. (1996). Measures of dependence and tests of independence. Statistics, 28:249-284.