Study of semiparametric copula models via divergences with bivariate censored data

Abstract

In this work, we study semiparametric copula models under bivariate censoring. Basing on divergences theory, we propose new estimates for the parameter of the considered model and we establish their weak consistency and asymptotic normality. We also propose tests of independence and goodness-of-fit tests for parametric families of copulas. A simulation study is conducted in order to illustrate the performance of the proposed estimates and tests.

Keywords:

• Bivariate censored data
• copulas
• divergences
• test of independence
• goodness-of-fit test

Acknowledgments

The author wishes to thank the reviewer for his valuable suggestions and comments.

Notes

1 The survival copula C_R of R is defined by $C_R(u_1,u_2)=u_1+u_2-1+C^{*}(1-u_1,1-u_2),$ where $C^{*}$ is the copula function of R.