Copulas: Concepts and novel applications

Metron

Volumn 61, Issue 3, 2003, Pages 323-353

  Owzar, Kouros ^a   Sen, Pranab Kumar ^b  

^a DUKE UNIVERSITY MEDICAL CENTER   (United States)

^b University of North Carolina at Chapel Hill   (United States)

Author keywords

Clinical Trials; Copula; Dependence; Microarrays; ROC; Semi parametrics; Survival

Indexed keywords

EID: 84860464016     PISSN: 00261424     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (68)

1. Bickel, P. J., Klaassen, C. A. J., Ritov, Y., and Wellner, J. A. (1994) Efficient and Adaptive Estimation for Semiparametric Models, Johns Hopkins University Press.
2. Bolthausen, E., Perkins, E., and van der Vaart, A. W. (2002) Lecture Notes in Probability and Statistics, vol. 1781 of Lecture Notes in Mathematics. Semiparametric Statistics, Springer- Verlag.
3. Capéraá, P., Fougéres, A. L., and Genest, C. (1997) A nonparametric estimation procedure for bivariate extreme value copulas, Biometrika, 84, 567-577.
4. Cifarelli, D. M., Conti, P. L., and Regazzini, E. (1996) On the Asymptotic Distribution of a General Measure of Monotone Dependence, The Annals of Statistics, 24, 1386-1399.
5. 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, 141-152.
6. Dabrowska, D. M. (1988) Kaplan-Meier Estimate on the Plane, The Annals of Statistics, 16, 1475- 1489.
7. Dabrowska, D. M. (1989) Kaplan-Meier Estimate on the Plane: Weak Convergence, LIL, and the Bootstrap, Journal of Multivariate Analysis, 29, 308-325.
8. Deheuvels, P. (1981a) A Kolmogorov-Smirnov type test for independence and multivariate samples (STMA V24 1687), Revue Roumaine de Mathematiques Pures et Appliquees, 26, 213-226.
9. Deheuvels, P. (1981b) Test for multivariate independence, In Topics in Applied Statistics-Proceedings of Statistics' 81 Canada Conference, 569-580.
10. DeLong, E. R., DeLong, D. M., and Clarke-Pearson, D. L. (1988) Comparing the areas under two or more correlated receiver operating characteristic curves: A nonparametric approach, Biometrics, 44, 837-845.
11. Efron, B. and Tibshirani, R. J. (1993) An Introduction to the Bootstrap, Chapman & Hall.
12. Falk, M. (1983) Relative efficiency and deficiency of kernel type estimators of smooth distribution functions, Statistica Neerlandica, 37, 73-83.
13. Fernholz, L. T. (1991) Almost sure convergence of smoothed empirical distribution functions, Scandinavian Journal of Statistics, 18, 255-262.
14. Fisher, N. I. (1997) Copulas, In S.Kotz, C. B. Read, and D. L. Banks, eds. Encyclopedia of Statistical Sciences, John Wiley & Sons.
15. Fisher, N. I. and Sen, P. K. (Eds) (1994) The Collected Works of Wassily Hoeffding, Springer- Verlag.
16. Fisher, N. I. and Switzer, P. (2001) Graphical Assessment of Dependence: Is a PictureWorth 100 Tests?, The American Statistician, 55, 3, 233-239.
17. Frank, M. J. (1979) On the simultaneous associativity of F(x, y) and x +y- F(x, y), Aequationes Mathematicae, 194-226.
18. Frees, E. W. and Valdez, E. A. (1998) Understanding relationships using copulas, North American Actuarial Journal, 2 (1), 1-25
19. Genest, C., Ghoudi, K., and Rivest, L. P. (1995) A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, 82, 543-552.
20. Genest, C. and Rivest, L. P. (1993) Statistical Inference Procedures for Bivariate Archimedean Copulas, Journal of the American Statistical Association, 88, 1034-1043.
21. Genest, C. and Rivest, L. P. (2001) On the multivariate probability integral transformation, Statistics and Probability Letters, 53 (4), 391-399.
22. Gill, R. D., van der Laan, M. J., and Wellner, J. A. (1995) Inefficient Estimators of the Bivariate Survival Function for Three Models, Annales de l'Institut Henri Poincare, Section B, Calcul des Probabilités et Statistique, 31, 545-597.
23. Gumbel, E. J. (1960) Bivariate Exponential Distributions, Journal of the American Statistical Association, 55, 698-707.
24. Gumbel, E. J. (1961) Bivariate Logistic Distributions, Journal of the American Statistical Association, 56, 335-349.
25. Hougaard, P. (2000) Analysis of Multivariate Survival Data, Springer-Verlag.
26. Joe, H. (1997) Multivariate Models and Dependence Concepts, Chapman & Hall.
27. Johnson, M. E. (1987) Multivariate Statistical Simulation, Wiley.
28. Jung, S. H., Wieand, S., and Cha, S. S. (1995) A statistic for comparing two correlated markers which are prognostic for time to an event, Statistics in Medicine, 14, 2217-2225.
29. Klaassen, C. A. J. and Wellner, J. A. (1997) Efficient Estimation in the Bivariate Normal Copula Model: Normal Margins Are Least Favourable, Bernoulli, 3, 55-77.
30. Kupla, T. (1999) On approximation of copulas, International Journal of Mathematics and Mathematical Sciences, 22, 259-269.
31. Lauprete, G. J., Samarov, A. M., and Welsch, R. E. (2002) Robust Portfolio Optimization, Metrika, 55 (2), 139-149.
32. Lee, A. J. (1993) Generating random binary deviates having fixed marginal distributions and specified degrees of association, The American Statistician, 47, 209-215.
33. Li, D. X. (2000) On default correlation: a copula function approach, Journal of Fixed Income, 9, 43-54.
34. Li, X., Mikusiński, P., and Taylor, M. D. (1998) Strong Approximations of Copulas, Journal of Mathematical Analysis and Applications, 225, 608-623.
35. Maguluri, G. (1993) Semiparametric estimation of association in a bivariate survival Function, The Annals of Statistics, 21, 1648-1662.
36. Mardia, K. V. (1970) Families of Bivariate Distributions. In: Griffin's Statistical Monographs and Courses No. 27, Charles Griffin.
37. Marshall, A. W. and Olkin, I. (1983) Domains of Attraction of Multivariate Extreme Value Distributions, The Annals of Probability, 11, 168-177.
38. Marshall, A. W. and Olkin, I. (1988) Families of multivariate distributions, Journal of the American Statistical Association, 83, 834-841.
39. Marshall, A. W. and Olkin, I. (1991) Multivariate Distributions Generated from Mixtures of Convolution and Product Families, In: Henry W. Block, Allan R., Sampson, and Savits, Thomas H. eds. Topics in Statistical Dependence, Institute of Mathematical Statistics.
40. Mikusinski, P., Sherwood, H., and Taylor, M. D. (1992) Shuffles of min, Stochastica, 13, 61-74.
41. Nelsen, R. (1998) An Introduction to Copulas, Springer-Verlag.
42. Oakes, D. (1982)AModel for Association in Bivariate Survival Data, Journal of the Royal Statistical Society, Series B, Methodological, 44, 414-422.
43. Oakes, D. (1986) Semiparametric Inference in a Model for Association in Bivariate Survival Data, Biometrika, 73, 353-361.
44. Oakes, D. (1994) Multivariate Survival Distributions, Journal of Nonparametric Statistics, 3, 343- 354.
45. O'Quigley, J. and Prentice, R. L. (1991) Nonparametric tests of association between survival time and continuously measured covariates: The logit-rank and associated procedures, Biometrics, 47, 117-127.
46. Pepe, M. S. (2000) Receiver operating characteristic methodology, Journal of the American Statistical Association, 95, 449, 308-311.
47. Prentice, R. L. and Cai, J. (1992) Covariance and Survivor Function Estimation Using Censored Multivariate Failure Time Data, Biometrika, 80, 711-712.
48. Reiss, R. D. (1981) Nonparametric estimation of smooth distribution functions, Scandinavian Journal of Stratistics, 8, 116-119.
49. Rivest, L. P. and Wells, M. T. (2001) A Martingale Approach to the Copula-graphic Estimator for the Survival Function Under Dependent Censoring, Journal of Multivariate Analysis, 79 (1), 138-155.
50. Scarsini, M. (1984) On measure of concordance, Stochastica, 8, 201-218.
51. Schweizer, B. (1991) Advances in Probability DistributionsWith Given Marginals, Vol. 67 of Mathematics and its applications, Thirty years of copula, Kluwer Academic Publishers.
52. Schweizer, B. and Sklar, A. (1983) Probabilistic metric spaces, Elsevier, North-Holland.
53. Schweizer, B. and Wolff, E. F. (1981) On nonparametric measures of dependence for random variables, The Annals of Statistics, 9, 879-885.
54. Shih, J. H. and Louis, T. A. (1995) Inferences on the association parameter in copula models for bivariate survival data, Biometrics, 51, 1384-1399.
55. Shih, J. H. and Louis, T. A. (1996) Tests of Independence for Bivariate Survival Data, Biometrics, 52, 1440-1449.
56. Sidak, Z., Sen, P. K., and Hajek, J. (1999) Theory of Rank Tests, Academic Press, second edition.
57. Sklar, A. (1959) Fonctions de repartition a n dimensions et leures marges, Publ. Inst. Statist. Univ. Paris, 8, 229-231.
58. Sklar, A. (1996) Random Variables, Distribution Functions, and Copulas - A Personal Look Backward and Forward. In: Distributions with Fixed Marginals and Related Topics (IMS Lecture Notes Monograph Series, Volume 28), Institute of Mathematical Statistics (Hayward).
59. Swets, J. A. and Pickett, R. M. (1982) Evaluation of diagnostic systems: Methods from signal detection theory, Academic Press.
60. van der Vaart, A. W. (1998) Asymptotic Statistics, Cambridge University Press.
61. van der Vaart, A. W. and Wellner, J. A. (1996) Weak convergence and empirical processes: with applications to statistics, Springer-Verlag.
62. Wang, S. (1998) Aggregation of correlated risk portfolios: model and algorithms, Proceedings of the Casualty Actuarial Society, LXXXV, 848-938.
63. Wang, W. and Wells, M. T. (2000) Model selection and semiparametric inference for bivariate failure-time data, Journal of the American Statistical Association, 95, 449, 73-76.
64. Winter, B. B. (1979) Convergence Rate of Perturbed Empirical Distribution Functions, Journal of Applied Probability, 16, 163-173.
65. Yamato, H. (1973) Uniform Convergence of an Estimator of a Distribution Function, Bull. Math. Statistics, 15, 69-78.
66. Zheng, M. and Klein, J. P. (1994) A Self-consistent Estimator of Marginal Survival Functions Based on Dependent Competing Risk Data and An Assumed Copula, Communications in Statistics, Part A - Theory and Methods, 23, 2299-2311.
67. Zheng, M. and Klein, J. P. (1995) Estimates of Marginal Survival for Dependent Competing Risks Based on An Assumed Copula, Biometrika, 82, 127-138.
68. Zheng, M. and Klein, J. P. (1996) Identifiability and Estimation of Marginal Survival Functions for Dependent Competing Risks Assuming the Copula Is Known. In: Lifetime Data Models in Reliability and Survival Analysis, Kluwer Academic (Dordrecht; Norwell, MA).