Non-parametric Copula Estimation Under Bivariate Censoring

作者：Gribkova Svetlana; Lopez Olivier^*

来源：Scandinavian Journal of Statistics, 2015, 42(4): 925-946.

DOI：10.1111/sjos.12144

• bivariate censoring
• bootstrap
• copula density
• copula function
• goodness-of-fit
• Kaplan-Meier estimator
• non-parametric estimation
• survival analysis

In this paper, we consider non-parametric copula inference under bivariate censoring. Based on an estimator of the joint cumulative distribution function, we define a discrete and two smooth estimators of the copula. The construction that we propose is valid for a large range of estimators of the distribution function and therefore for a large range of bivariate censoring frameworks. Under some conditions on the tails of the distributions, the weak convergence of the corresponding copula processes is obtained in l(infinity) ([0, 1](2)).We derive the uniform convergence rates of the copula density estimators deduced from our smooth copula estimators. Investigation of the practical behaviour of these estimators is performed through a simulation study and two real data applications, corresponding to different censoring settings. We use our non-parametric estimators to define a goodness-of-fit procedure for parametric copula models. A new bootstrap scheme is proposed to compute the critical values.

• 出版日期2015-12