Efficient estimation of semiparametric multivariate copula models

Journal of the American Statistical Association

Volumn 101, Issue 475, 2006, Pages 1228-1240

  Chen, Xiaohong ^a   Fan, Yanqin ^b   Tsyrennikov, Viktor ^a  

^a NEW YORK UNIVERSITY   (United States)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

Copula dependence parameter; Efficiency bound; Marginal distribution; Prior information; Sieve maximum likelihood

Indexed keywords

EID: 33748864740     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214506000000311     Document Type: Review

References (42)

1. Ai, C., and Chen, X. (2003), "Efficient Estimation of Models With Conditional Moment Restrietions Containing Unknown Functions," Econometrica, 71, 1795-1843.
2. Barron, A., and Sheu, C. (1991), "Approximation of Density Functions by Sequences of Exponential Families," The Annals of Statistics, 19, 1347-1369.
3. Bickel, P., Klaassen, C., Ritov, Y., and Wellner, J. (1993), Efficient and Adaptive Estimation for Semiparametric Models, Baltimore: John Hopkins University Press.
4. Chen, X., and Fan, Y. (2005), "Estimation and Model Selection of Semiparametric Copula-Based Multivuriate Dynamic Models Under Copula Misspecification," Journal of Econometrics, available online 6 Sept. 2005.
5. _ (2006), "Estimation of Copula-Based Semiparametric Time Series Models," Journal of Econometrics, 130, 307-335.
6. Chen, X., Fan, Y., and Tsyrennikov, V. (2005), "Efficient Estimation of Semiparametric Multivuriate Copula Models," working paper, New York University.
7. Chen, X., and White, H. (1999), "Improved Rates and Asymptotic Normality for Nonparametric Neural Network Estimators," IEEE Transactions on Information Theory, 45, 682-691.
8. Chui, C. K. (1992), An Introduction to Wavelets, San Diego, CA: Academic Press.
9. Clayton, D. (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.
10. Clayton, D., and Cuzick, J. (1985), "Mullivariate Generalizations of the Proportional Hazards Model" (with discussion), Journal of the Koval Statistical Society, Ser. A, 148, 82-117.
11. Coppejans, M., and Gallant, A. R. (2002), "Cross-Validated SNP Density Estimates," Journal of Econometrics, 110, 27-65.
12. Embrechts, P., McNeil, A., and Straumann, D. (2002), "Correlation and Dependence Properties in Risk Management: Properties and Pitfalls," in Risk Management: Value at Risk and Beyond, ed. M. Dempster, Cambridge, U.K.: Cambridge University Press, pp. 176-223.
13. Frees, E. W., and Valdez, E. A. (1998), "Understanding Relationships Using Copulas," North American Actuarial Journal, 2, 1-25.
14. Gallant, A. R., and Nychka, D. (1987), "Semi-Non-Parametric Maximum Likelihood Estimation," Econometrica, 55, 363-390.
15. Geman, S., and Hwang, C. (1982), "Nonparametric Maximum Likelihood Estimation by the Method of Sieves," The Annuls of Statistics, 10, 401-414.
16. Genest, C. (1987), "Frank's Family of Bivariate Distributions," Biometrika, 74, 549-555.
17. Genest, C., Ghoudi, K., and Rivest, L.-P. (1995), "A Semiparametric Estimation Procedure of Dependence Parameters in Multivariate Families of Distributions," Biometrika, 82, 534-552.
18. Genest, C., and Werker, B. (2002), "Conditions for the Asymptotic Semiparametric Efficiency of an Omnibus Estimator of Dependence Parameters in Copula Models," in Proceedings of the Conference on Distributions With Given Marginals and Statistical Modelling, eds. C. M. Cuadras and J. A. Rodríguez Lallena, Dordrecht: Kluwer Academic Publishers, pp. 103-112.
19. Granger, C. W. J., Teräsvirta, T., and Patton, A, (2006), "Commun Factors in Conditional Distributions," Journal of Econometrics, 132, 43-57.
20. Grenander, U. (1981), Abstract Inference, New York: Wiley.
21. Heckman, J. J., and Honoré, B. E. (1989), "The Identifiability of the Competing Risks Model," Biometrika, 76, 325-330.
22. Joe, H. (1997), Multivariate Models find Dependence Concepts. Boca Raton, FL: Chapman & Hall/CRC.
23. Klaassen, C., and Wellner, J. (1997), "Efficient Estimation in the Bivariate Normal Copula Model: Normal Margins Are Least Favorable," Bernoulli, 3, 55-77.
24. Lee, L. (1983), "Generalized Econometric Models With Selectivity," Econometrica, 51, 507-512.
25. Maguluri, G. (1993), "Semiparametric Estimation of Association in a Bivariate Survival Function," The Annals of Statistics, 21, 1648-1662.
26. Nelsen, R. B. (1999), An Introduction to Copulas, New York: Springer-Verlag.
27. Oakes, D. (1982), "A Model for Association in Bivariate Survival Data," Journal of the Royal Statistical Society, Ser. B, 44, 414-422.
28. _ (1986), "Semiparametric Inference in a Model for Association in Bivariate Survival Data," Biometrika, 73, 353-361.
29. _ (1989), "Bivariate Survival Models Induced by Frailties," Journal of the American Statistical Association, 84, 487-493.
30. _ (1994), "Multivariate Survival Distributions," Journal of Nonparametric Statistics, 3, 343-354.
31. Patton, A. J. (2004), "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, 2, 130-168.
32. Robinson, P. (1988), "Root-n-Consistent Semiparametric Regression," Econometrica, 56, 931-954.
33. Schumaker, L. (1981), Spline Functions: Basic Theory, New York: Wiley.
34. Shen, X. (1997), "On Methods of Sieves and Penalization," The Annals of Statistics, 25, 2555-2591.
35. Shen, X., and Wong, W. (1994), "Convergence Rate of Sieve Estimates," The Annals of Statistics, 22, 580-615.
36. Shen, X., and Ye, J. (2002), "Adaptive Model Selection," Journal of the American Statistical Association, 97, 210-221.
37. Shih, J. H., and Louis, T. A. (1995), "Inferences on the Association Parameter in Copula Models for Bivariate Survival Data," Biometrics, 51, 1384-1399.
38. Sklar, A. (1959), "Fonctions de répartition à n dimensionset leurs marges," Publications de l'Institut de Statistique de L'Univerité de Paris, 8, 229-231.
39. Stone, C. (1982), "Optimal Global Rates of Convergence for Nonparametric Regression," The Annals of Statistics, 10, 1040-1053.
40. _ (1990), "Large-Sample Inference for Log-Spline Models," The Annals of Statistics, 18, 717-741.
41. Van de Geer, S. (2000), Empirical Processes in M-Estimation, Cambridge, U.K.: Cambridge University Press.
42. Wong, W., and Shen, X. (1995), "Probability Inequalities for Likelihood Ratios and Convergence Rates for Sieve MLEs," The Annals of Statistics, 23, 339-362.