A semiparametric estimator of the bivariate distribution function for censored gap times.

@article{deUalvarez2011ASE,
  title={A semiparametric estimator of the bivariate distribution function for censored gap times.},
  author={Jacobo de U{\~n}a-{\'A}lvarez and Ana Paula Amorim},
  journal={Biometrical journal. Biometrische Zeitschrift},
  year={2011},
  volume={53 1},
  pages={
          113-27
        }
}
Let (T(1), T(2)) be gap times corresponding to two consecutive events, which are observed subject to random right-censoring. In this paper, a semiparametric estimator of the bivariate distribution function of (T(1), T(2)) and, more generally, of a functional E [φ(T(1),T(2))] is proposed. We assume that the probability of censoring for T(2) given the (possibly censored) gap times belongs to a parametric family of binary regression curves. We investigate the conditions under which the introduced… 
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References

SHOWING 1-10 OF 29 REFERENCES
A note on the nonparametric estimation of the bivariate distribution under dependent censoring
Consider a random vector (T-1, T-2), and assume that both T-1 and T-2 are subject to random right censoring. We propose new estimators of the bivariate and marginal distributions of T-1 and T-2. The…
A simple estimator of the bivariate distribution function for censored gap times
Nonparametric estimation of the conditional distribution function in a semiparametric censorship model
Locally Efficient Estimation of a Multivariate Survival Function in Longitudinal Studies
We consider estimation of the joint distribution of multivariate survival times T = (T1,…,Tk), which are subject to right-censoring by a common censoring variableC. Two estimators are proposed: an…
On semiparametric random censorship models
The central limit theorem under semiparametric random censorship models
Semiparametric censorship model with covariates
In real applications, we may be confronted with the problem of informative censoring. Koziol-Green model is commonly used to model the possible information contained in the informative censoring.…
Nonparametric estimation of the gap time distributions for serial events with censored data
Summary In many follow-up studies, each subject can potentially experience a series of events, which may be repetitions of essentially the same event or may be events of entirely diVerent natures.…
Bootstrapping the Kaplan—Meier Estimator
Abstract Randomly censored data consist of iid pairs of observations (Xi, δi), i = 1, …, n; if δ i = 0, Xi denotes a censored observation, and if δ i = 1, Xi denotes an exact “survival” time, which…
Nonparametric Estimation With Recurrent Event Data
The problem of nonparametric estimation for the distribution function governing the time to occurrence of a recurrent event in the presence of censoring is considered. We derive Nelson–Aalen and…
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3
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