TY - JOUR
T1 - Properties of the marginal survival functions for dependent censored data under an assumed Archimedean copula
AU - Wang, Antai
N1 - Funding Information:
The author thanks Christian Genest, an Associate Editor, and two anonymous reviewers for valuable comments that led to great improvement of this paper. This research was supported by Grant Nos. DMS1106608 and DMS1343889 from the National Science Foundation .
PY - 2014/8
Y1 - 2014/8
N2 - Given a random sample from a dependent censored variable ( X, δ) = ( min ( T, C) , 1 ( T < C) ) , general formulas are given for possible marginal survival functions of the failure time T and the censoring time C under the assumption that their underlying copula is Archimedean. These formulas are used to establish the relationship between these possible survival functions, along with useful identifiability results. A new estimator of the marginal survival functions is also proposed, under the assumption that the underlying Archimedean copula is known. Bias formulas for this estimator and other existing estimators are derived. Simulation studies show that the new estimator is comparable with the copula-graphic estimator proposed by Zheng and Klein (1995) and Rivest and Wells (2001), as well as with the estimator of Zheng and Klein (1994) under the Archimedean copula assumption.
AB - Given a random sample from a dependent censored variable ( X, δ) = ( min ( T, C) , 1 ( T < C) ) , general formulas are given for possible marginal survival functions of the failure time T and the censoring time C under the assumption that their underlying copula is Archimedean. These formulas are used to establish the relationship between these possible survival functions, along with useful identifiability results. A new estimator of the marginal survival functions is also proposed, under the assumption that the underlying Archimedean copula is known. Bias formulas for this estimator and other existing estimators are derived. Simulation studies show that the new estimator is comparable with the copula-graphic estimator proposed by Zheng and Klein (1995) and Rivest and Wells (2001), as well as with the estimator of Zheng and Klein (1994) under the Archimedean copula assumption.
KW - 62N01
KW - Archimedean copula models
KW - Copula-graphic estimator
KW - Dependent censored data
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U2 - 10.1016/j.jmva.2014.04.009
DO - 10.1016/j.jmva.2014.04.009
M3 - Article
AN - SCOPUS:84899889558
SN - 0047-259X
VL - 129
SP - 57
EP - 68
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -