Hostname: page-component-84b7d79bbc-dwq4g Total loading time: 0 Render date: 2024-08-04T18:38:34.609Z Has data issue: false hasContentIssue false
  • English
  • Français

A MODEL SELECTION TEST FOR BIVARIATE FAILURE-TIME DATA

Published online by Cambridge University Press:  05 April 2007

Xiaohong Chen  and
Yanqin Fan
Xiaohong Chen
Affiliation:
New York University
Yanqin Fan
Affiliation:
Vanderbilt University
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we address two important issues in semiparametric survival model selection for censored data generated by the Archimedean copula family: method of estimating the parametric copulas and data reuse. We demonstrate that for selection among candidate copula models that might all be misspecified, estimators of the parametric copulas based on minimizing the selection criterion function may be preferred to other estimators. To handle the issue of data reuse, we put model selection in the context of hypothesis testing and propose a simple test for model selection from a finite number of parametric copulas. Results from a simulation study and two empirical illustrations confirm our theoretical findings.We thank the editor Peter Phillips, three anonymous referees, and Hal White for their comments, which greatly improved the paper. An earlier version of this paper was presented at the 2005 World Congress Meetings of the Econometric Society, the 2005 Joint Statistical Meetings, the University of Waterloo, and the University of Western Ontario. Chen acknowledges support from the National Science Foundation and the C.V. Starr Center at NYU. Fan acknowledges support from the National Science Foundation. We thank Demian Pouzo for excellent research assistance on the numerical work in this paper and Weijing Wang for providing us with the Fortran code for computing the bivariate Kaplan–Meier estimator of Dabrowska (1988).

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 3 , June 2007 , pp. 414 - 439
Copyright
© 2007 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Barbe, P., A. Genest, K. Ghoudi, & R. Bruno (1996) On Kendall's process. Journal of Multivariate Analysis 58, 197–229.Google Scholar
Chen, X. & Y. Fan (2005) Pseudo-likelihood ratio tests for model selection in semiparametric multivariate copula models. Canadian Journal of Statistics 33, 389–414.Google Scholar
Chen, X. & Y. Fan (2006a) Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification. Journal of Econometrics 135, 125–154.Google Scholar
Chen, X. & Y. Fan (2006b) Estimation of copula-based semiparametric time series models. Journal of Econometrics 130, 307–335.Google Scholar
Chen, X., Y. Fan, & A. Patton (2003) Simple Tests for Models of Dependence between Multiple Financial Time Series: With Applications to U.S. Equity Returns and Exchange Rates. Manuscript, New York University, Vanderbilt University, and London School of Economics.
Chen, X., Y. Fan, & V. Tsyrennikov (2006) Efficient estimation of semiparametric multivariate copula models. Journal of the American Statistical Association 101, 1228–1240.Google Scholar
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.Google Scholar
Clayton, D. & J. Cuzick (1985) Multivariate generalizations of the proportional hazards model (with discussion). Journal of the Royal Statistical Society, Series A 148, 82–117.Google Scholar
Dabrowska, D.M. (1988) Kaplan-Meier estimates on the plane. Annals of Statistics 16, 1475–1489.Google Scholar
Dabrowska, D.M. (1989) Kaplan-Meier estimate on the plane: Weak convergence, LIL, and the bootstrap. Journal of Multivariate Analysis 29, 308–325.Google Scholar
Danahy, D.J., D.T. Burwell, W.S. Aranow, & R. Prakash (1977) Sustained henodynamic and antianginal effect of high-dose oral isosorbide dinitrate. Circulation 55, 381–387.Google Scholar
Embrechts, P., A. McNeil, & D. Straumann (2002) Correlation and dependence properties in risk management: Properties and pitfalls. In M. Dempster (ed.), Risk Management: Value at Risk and Beyond, pp. 176–223. Cambridge University Press.
Fermanian, J.-D. (2005) Goodness of fit tests for copulas. Journal of Multivariate Analysis 95, 119–152.Google Scholar
Frees, Edward W. & E.A. Valdez (1998) Understanding relationships using copulas. North American Actuarial Journal 2, 1–25.Google Scholar
Genest, C. (1987) Frank's family of bivariate distributions. Biometrika 74, 549–555.Google Scholar
Genest, C., K. Ghoudi, & L.-P. Rivest (1995) A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82, 543–552.Google Scholar
Genest, C., J.-F. Quessy, & B. Rémillard (2006) Goodness-of-fit procedures for copula models based on the integral probability transformation. Scandinavian Journal of Statistics 33, 337–366.Google Scholar
Genest, C. & L.-P. Rivest (1993) Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association 88, 1034–1043.Google Scholar
Genest, C. & B. Werker (2002) Conditions for the asymptotic semiparametric efficiency of an omnibus estimator of dependence parameters in copula models. In C.M. Cuadras, J. Fortiana, & J.A. Rodríguez Lallena (eds.), Distributions with Given Marginals and Statistical Modelling, pp. 103–112. Kluwer.
Gonçalves, S. & H. White (2004) Maximum likelihood and the bootstrap for nonlinear dynamic models. Journal of Econometrics 119, 199–219.Google Scholar
Granger, C.W.J., T. Teräsvirta, & A. Patton (2006) Common factors in conditional distributions for bivariate time series. Journal of Econometrics 132, 43–57.Google Scholar
Heckman, J.J. & B.E. Honoré (1989) The identifiability of the competing risks model. Biometrika 76, 325–330.Google Scholar
Hougaard, P. (1986) Survival models for heterogeneous populations derived from stable distributions. Biometrika 73, 387–396.Google Scholar
Hu, L. (2006) Dependence patterns across financial markets: A mixed copula approach. Applied Financial Economics 16, 717–729.Google Scholar
Joe, H. (1997) Multivariate Models and Dependence Concepts. Chapman and Hall/CRC.
Lee, L. (1983) Generalized econometric models with selectivity. Econometrica 51, 507–512.Google Scholar
Lin, D. & Z. Ying (1993) A simple nonparametric estimator of the bivariate survival function under univariate censoring. Biometrika 80, 573–581.Google Scholar
McGilchrist, C.A. & C.W. Aisbett (1991) Regression with frailty in survival analysis. Biometrics 47, 461–466.Google Scholar
Nelsen, R.B. (1997) Dependence and order in families of Archimedean copulas. Journal of Multivariate Analysis 60, 111–122.Google Scholar
Nelsen, R.B. (1999) An Introduction to Copulas. Springer-Verlag.
Oakes, D. (1982) A concordance test for independence in the presence of bivariate censoring. Biometrics 38, 451–455.Google Scholar
Oakes, D. (1986) Semiparametric inference in a model for association in bivariate survival data. Biometrika 73, 353–361.Google Scholar
Oakes, D. (1989) Bivariate survival models induced by frailties. Journal of the American Statistical Association 84, 487–493.Google Scholar
Oakes, D. (1994) Multivariate survival distributions. Journal of Nonparametric Statistics 3, 343–354.Google Scholar
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.Google Scholar
Patton, A.J. (2006) Modeling asymmetric exchange rate dependence. International Economic Review 47, 527–556.Google Scholar
Romano, J.P. & M. Wolf (2005) Stepwise multiple testing as formalized data snooping. Econometrica 73, 1237–1282.Google Scholar
Shih, J. & T. Louis (1995) Inferences on the association parameter in copula models for bivariate survival data. Biometrics 51, 1384–1399.Google Scholar
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.Google Scholar
Van der Vaart, A. & J. Wellner (1996) Weak Convergence and Empirical Processes: With Applications to Statistics. Springer-Verlag.
Vuong, Q.H. (1989) Likelihood ratio test for model selection and non-nested hypotheses. Econometrica 57, 307–333.Google Scholar
Wang, W. & M. Wells (2000) Model selection and semiparametric inference for bivariate failure-time data (with Comment by V. Peña and Rejoinder by the authors). Journal of the American Statistical Association 95, 62–76.Google Scholar
White, H. (1994) Estimation, Inference and Specification Analysis. Cambridge University Press.
White, H. (2000) A reality check for data snooping. Econometrica 68, 1097–1126.Google Scholar