Nonparametric Copula Estimation Under Bivariate Censoring

• Activity Number: 518
• Type: Invited
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Journal of Nonparametric Statistics
• Author(s): Olivier Lopez* and Svetlana Gribkova
• Companies: CREST-Ensai and Université Pierre et Marie Curie
• Keywords: copula ; censoring ; survival analysis ; nonparametric estimation

Abstract

We consider nonparametric 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. Under some conditions on the tails of the distributions, the weak convergence of the corresponding copula processes is obtained in $l^{\infty}([0,1]^2).$ The copula density estimators, which can be deduced from our smooth copula estimators, are shown to be uniformly consistent, and their convergence rate is obtained. Goodness-of-fit procedures based on these estimators are considered, and applied to a real data application to joint lifetime modeling in a life-insurance portfolio.