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Non‐parametric Copula Estimation Under Bivariate Censoring
Author(s) -
Gribkova Svetlana,
Lopez Olivier
Publication year - 2015
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12144
Subject(s) - copula (linguistics) , estimator , mathematics , bivariate analysis , censoring (clinical trials) , parametric statistics , joint probability distribution , weak convergence , econometrics , statistics , inference , nonparametric statistics , marginal distribution , computer science , random variable , computer security , artificial intelligence , asset (computer security)
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.