Likelihood ratio procedures and tests of fit in parametric and semiparametric copula models with censored data

Lifetime Data Analysis

Volumn 17, Issue 3, 2011, Pages 386-408

  Yilmaz, Yildiz E ^a   Lawless, Jerald F ^b  

^a MOUNT SINAI HOSPITAL   (Canada)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Maximum likelihood; Model misspecification; Pseudolikelihood; Semiparametric estimation

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; BIOMETRY; COMPARATIVE STUDY; COMPUTER SIMULATION; DIABETIC RETINOPATHY; HUMAN; LASER COAGULATION; METHODOLOGY; STANDARD; STATISTICAL MODEL; VISUAL ACUITY;

BIOMETRY; COMPUTER SIMULATION; DIABETIC RETINOPATHY; HUMANS; LIGHT COAGULATION; LIKELIHOOD FUNCTIONS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; VISUAL ACUITY;

EID: 79958268278     PISSN: 13807870     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10985-011-9192-2     Document Type: Article

References (43)

1. Andersen PK, Ekstrom CT, Klein JP, Shu Y, Zhang M-J (2005) A class of goodness of fit tests for a copula based on bivariate right-censored data. Biom J 47: 815-824.
2. Bailey KR (1984) Asymptotic equivalence between the Cox estimator and the general ML estimators of regression and survival parameters in the Cox model. Ann Stat 12: 730-736.
3. Chen X, Fan Y (2005) Pseudo-likelihood ratio tests for semiparametric multivariate copula model selection. Can J Stat 33: 389-414.
4. Chen SX, Huang T-M (2007) Nonparametric estimation of copula functions for dependence modelling. Can J Stat 35: 265-282.
5. Chen X, Fan Y, Tsyrennikov V (2006) Efficient estimation of semiparametric multivariate copula models. J Am Stat Assoc 101: 1228-1240.
6. 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.
7. Cox DR, Hinkley DV (1974) Theoretical statistics. Chapman & Hall, London.
8. Fermanian J-D (2005) Goodness-of-fit tests for copulas. J Multivar Anal 95: 119-152.
9. Frank MJ (1979) On the simultaneous associativity of F(x, y) and x + y-F(x, y). Aequ Math 19: 194-226.
10. Frees EW, Valdez EA (1998) Understanding relationships using copulas. N Am Actuar J 2: 1-25.
11. Genest C, Rémillard B (2008) Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models. Ann Inst Henri Poincaré Probab Stat 44: 1096-1127.
12. Genest C, Rivest LP (1993) Statistical inference procedures for bivariate Archimedean copulas. J Am Stat Assoc 88: 1034-1043.
13. Genest C, Ghoudi K, Rivest L-P (1998) Comment on "Understanding relationships using copulas," by EW Frees and EA Valdez. N Am Actuar J 2: 143-149.
14. Genest C, Quessy J-F, Rémillard B (2006a) Goodness-of-fit procedures for copula models based on the probability integral transformation. Scand J Stat 33: 337-366.
15. Genest C, Quessy J-F, Rémillard B (2006b) On the joint asymptotic behaviour of two rank-based estimators of the association parameter in the gamma frailty model. Stat Probab Lett 76: 10-18.
16. Genest C, Rémillard B, Beaudoin D (2009) Goodness-of-fit tests for copulas: a review and a power study. Insur Math Econ 44: 199-213.
17. Gentleman R, Vandal AC (2002) Nonparametric estimation of the bivariate CDF for arbitrarily censored data. Can J Stat 30: 557-571.
18. Glidden DV (2000) A two-stage estimator of the dependence parameter for the Clayton-Oakes model. Lifetime Data Anal 6: 141-156.
19. Glidden DV, Self SG (1999) Semiparametric likelihood estimation in the Clayton-Oakes failure time model. Scand J Stat 26: 363-372.
20. Gumbel EJ (1960) Distribution des valeurs extrêmes en plusieurs dimensions. Publications de l'Institut de statistique de l'Université de Paris 9: 171-173.
21. He W, Lawless JF (2003) Flexible maximum likelihood methods for bivariate proportional hazards models. Biometrics 59: 837-848.
22. Hougaard P, Harvald B, Holm NV (1992) Measuring the similarities between lifetimes of adult Danish twins born between 1881-1930. J Am Stat Assoc 87: 17-24.
23. Hsieh J-J, Wang W, Ding AA (2008) Regression analysis based on semicompeting risks data. J R Stat Soc B 70: 3-20.
24. Hsu L, Gorfine M (2006) Multivariate survival analysis for case-control family data. Biostatistics 7: 387-398.
25. Huster WJ, Brookmeyer R, Self SG (1989) Modeling paired survival data with covariates. Biometrics 45: 145-156.
26. Joe H (1997) Multivariate models and dependence concepts. Chapman & Hall, London.
27. Kim G, Silvapulle MJ, Silvapulle P (2007) Comparison of semiparametric and parametric methods for estimating copulas. Comput Stat Data Anal 51: 2836-2850.
28. Lawless JF (2003) Statistical models and methods for lifetime data, 2nd edn. Wiley, Hoboken.
29. Li DX (2000) On default correlation: a copula function approach. J Fixed Income 9: 43-54.
30. Li Y, Prentice RL, Lin X (2008) Semiparametric maximum likelihood estimation in normal transformation models for bivariate survival models. Biometrika 95: 947-960.
31. Liang K-Y, Self SG (1996) On the asymptotic behaviour of the pseudolikelihood ratio test statistic. J R Stat Soc B 58: 785-796.
32. Lin DY, Sun W, Ying Z (1999) Nonparametric estimation of the gap time distribution for serial events with censored data. Biometrika 86: 59-70.
33. Martinussen T, Pipper CB (2005) Estimation in the positive stable frailty Cox proportional hazards model. Lifetime Data Anal 11: 99-115.
34. Murphy SA, van der Vaart AW (1997) Semiparametric likelihood ratio inference. Ann Stat 25: 1471-1509.
35. Nelsen RB (2006) An introduction to copulas, 2nd edn. Springer, New York.
36. Oakes D (1989) Bivariate survival models induced by frailties. J Am Stat Assoc 84: 487-493.
37. Pipper CB, Martinussen T (2003) A likelihood based estimating equation for the Clayton-Oakes model with marginal proportional hazards. Scand J Stat 30: 509-521.
38. Self GS, Liang K-Y (1987) Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J Am Stat Assoc 82: 605-610.
39. Shih JH (1998) A goodness-of-fit test for association in a bivariate survival model. Biometrika 85: 189-200.
40. Shih JH, Louis TA (1995) Inferences on the association parameter in copula models for bivariate survival data. Biometrics 51: 1384-1399.
41. Sklar A (1959) Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institut de statistique de l'Université de Paris 8: 229-231.
42. Wang W, Wells MT (2000) Model selection and semiparametric inference for bivariate failure-time data. J Am Stat Assoc 95: 62-72.
43. White H (1982) Maximum likelihood estimation of misspecified models. Econometrica 50: 1-25.