Copula analysis of mixture models

Computational Statistics

Volumn 27, Issue 3, 2012, Pages 427-457

  Vrac, M ^a   Billard, L ^b   Diday, E ^c   Chedin A ^d  

^a LABORATOIRE DES SCIENCES DU CLIMAT ET DE L ENVIRONNEMENT   (France)

^b UNIVERSITY OF GEORGIA   (United States)

^c UNIVERSITÉ PARIS DAUPHINE   (France)

^d ECOLE POLYTECHNIQUE   (France)

Author keywords

Classification of distributions; Copulas; Data distributions; Dynamical clustering; Estimation; Mixture model

Indexed keywords

EID: 84864391134     PISSN: 09434062     EISSN: 16139658     Source Type: Journal    
DOI: 10.1007/s00180-011-0266-0     Document Type: Article

References (53)

1. Achard V (1991) Trois Problemes dés de d'Analyse 3D de la Structure Thermodynamique de l'Atmosphére par Satellite: Mesure du Contenu en Ozone; Classification des Masses d'Air; Modélisation Hyper Rapide du Transfert Radiatif. Ph. D. Dissertation, University of Paris.
2. Ali MM, Mikhail NN, Haq MS (1978) A class of bivariate distributions including the bivariate logistic. J Multivar Anal 8: 405-412.
3. Arabie P, Carroll JD (1980) MAPCLUS: a mathematical programming approach to fitting the ADCLUS model. Psychometrika 45: 211-235.
4. Banfield JD, Raftery AE (1993) Model-based Gaussian and non-Gaussian clustering. Biometrics 49: 803-821.
5. Bishop CM (1995) Neural networks for pattern recognition. Clarendon Press, Oxford.
6. Bock HH (1998) Clustering and neural networks. In: Rizzi A, Vichi M, Bock HH (eds) Advances in data science and classification. Springer, Berlin, pp 265-277.
7. Bock RD, Gibbons RD (1996) High-dimensional multivariate probit analysis. Biometrics 52: 1183-1194.
8. Brossier G (1990) Piecewise hierarchical clustering. J Classif 7: 197-216.
9. Celeux G, Diday E, Govaert G, Lechevallier Y, Ralambondrainy H (1989) Classification automatique des données. Dunod Informatique, Paris.
10. Celeux G, Diebolt J (1986) L'Algorithme SEM: Un algorithme d'apprentissage probabiliste pour la reconnaissance de mélange de densities. Revue de Statistiques Appliquées 34: 35-51.
11. Celeux G, Govaert G (1992) A classification EM algorithm for clustering and two stochastic versions. Comput Stat Data Anal 14: 315-332.
12. Celeux G, Govaert G (1993) Comparison of the mixture and the classification maximum likelihood in cluster analysis. J Stat Comput Simul 47: 127-146.
13. Chédin A, Scott N, Wahiche C, Moulinier P (1985) The improved initialization inversion method: a high resolution physical method for temperature retrievals from satellites of tiros-n series. J Appl Meteorol 24: 128-143.
14. Chan JSK, Kuk AYC (1997) Maximum likelihood estimation for probit-linear mixed models with correlated random effects. Biometrics 53: 86-97.
15. Clayton DG (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.
16. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc B 39: 1-38.
17. Diday E (1984) Une représentation visuelle des classes empietantes: les pyramides. Rapport de Recherche 291 INRIA.
18. Diday E (2001) A generalization of the mixture decomposition problem in the symbolic data analysis framework. Rapport de Recherche, CEREMADE 112: 1-14.
19. Diday E, Schroeder A, Ok Y (1974) The dynamic clusters method in pattern recognition. In: Proceedings of international federation for information processing congress. Elsevier, New York, pp 691-697.
20. Diday E, Vrac M (2005) Mixture decomposition of distributions by copulas in the symbolic data analysis framework. Discrete Appl Math 147: 27-41.
21. Fraley C, Raftery AE (2002) Model-based clustering, discriminant analysis and density estimation. J Am Stat Assoc 97: 611-631.
22. Frank MJ (1979) On the simultaneous associativity of F(x, y) and x + y - F(x, y). Aequationes Mathematicae 19: 194-226.
23. Genest C, Ghoudi K (1994) Une famille de lois bidimensionelles insolite. Compte Rendus Academy Sciences Paris I 318: 351-354.
24. Genest C, MacKay J (1986) The joy of copulas: bivariate distributions with uniform marginals. Am Stat 40: 280-283.
25. Genest C, Rivest LP (1993) Statistical inference procedures for bivariate Archimedean copulas. J Am Stat Assoc 88: 1034-1043.
26. Gordon A (1999) Classification. 2nd edn. Chapman and Hall, Boca Raton.
27. Hartigan JA, Wong MA (1979) Algorithm AS136. A k-means clustering algorithm. Appl Stat 28: 100-108.
28. Hillali Y (1998) Analyse et modélisation des données probabilistes: Capacités et lois multidimensionelles. Ph. D. Dissertation, University of Paris.
29. Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice Hall, New Jersey.
30. James GM, Sugar CA (2003) Clustering for sparsely sampled functional data. J Am Stat Assoc 98: 397-408.
31. Kuk AYC, Chan JSK (2001) Three ways of implementing the EM algorithm when parameters are not identifiable. Biometric J 43: 207-218.
32. Li LA, Sedransk N (1988) Mixtures of distributions: a topological approach. Ann Stat 16: 1623-1634.
33. McLachlan G, Peel D (2000) Finite mixture models. Wiley, New York.
34. Meng XL, Rubin DB (1991) Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. J Am Stat Assoc 86: 899-909.
35. Nelsen RB (1999) An introduction to copulas. Springer, New York.
36. Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33: 1065-1076.
37. Prakasa Rao BLS (1983) Nonparametric functional estimation. Academic Press, New York.
38. Redner RA, Walker H (1984) Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev 26: 195-239.
39. Richardson S, Green PJ (1997) On Bayesian analysis of mixtures with an unknown number of components. J R Stat Soc Ser B 59: 731-792.
40. Schroeder A (1976) Analyse d'un mélange de distributions de probabilité de měme type. Revue de Statistiques Appliquées 24: 39-62.
41. Schweizer B, Sklar A (1983) Probabilistic metric spaces. North-Holland, New York.
42. Schweizer B (1984) Distributions are the numbers of the future. In: diNola A, Ventre A (eds) Proceedings of the mathematics of fuzzy systems meeting, Naples, Italy. University of Naples, Naples, pp 137-149.
43. Scott AJ, Symons MJ (1971) Clustering methods based on likelihood ratio criteria. Biometrics 27: 387-397.
44. Silverman BW (1986) Density estimation for statistics and data analysis. Chapman and Hall, London.
45. Sklar A (1959) Fonction de répartition a n dimensions et leurs marges. Institute Statistics Université de Paris 8: 229-231.
46. Symons MJ (1981) Clustering criteria and multivariate normal mixtures. Biometrics 37: 35-43.
47. Tanner MA, Wong WH (1987) The calculation of posterior distribution by data augmentation (with discussion). J Am Stat Assoc 82: 528-550.
48. Titterington DM, Smith AFM, Makov UE (1985) Statistical analysis of finite mixture distributions. Wiley, New York.
49. Vrac M (2002) Analyse et modélisation de données probabilistes par decomposition de mélange de copules et application á une base de données climatologiques. Ph. D. Dissertation, University of Paris.
50. Vrac M, Chédin A, Diday E (2005) Clustering a global field of atmospheric profiles by mixture decomposition of copulas. J Atmos Ocean Technol 22: 1445-1459.
51. Wei GCG, Tanner MA (1990) A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms. J Am Stat Assoc 85: 699-704.
52. Winsberg S, DeSoete G (1999) Latent class models for time series analysis. Appl Stoch Models Bus Ind 15: 183-194.
53. Yakowitz SJ, Spragins LD (1968) On the identifiability of finite mixtures. Ann Math Stat 39: 209-214.