Non-parametric Copula Estimation Under Bivariate Censoring

Svetlana Gribkova and Olivier Lopez

Scandinavian Journal of Statistics, 2015, vol. 42, issue 4, 925-946

Abstract: type="main" xml:id="sjos12144-abs-0001"> 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-super-∞([0,1]-super-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.

Date: 2015
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