Non‐parametric Copula Estimation Under Bivariate Censoring. (14th April 2015)

• Record Type: Journal Article
• Authors: Gribkova, Svetlana; Lopez, Olivier
• Is Part Of: Scandinavian journal of statistics. Volume 42:Number 4(2015:Dec.)
• Page Start: 925
• Page End: 946
• Publication Date: 2015-04-14
• Subjects: bivariate censoring -- bootstrap -- copula density -- copula function -- goodness‐of‐fit -- Kaplan–Meier estimator -- non‐parametric estimation -- survival analysis; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12144
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: 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 ∞ ([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.