TY  - JOUR
A1  - Dikta, Gerhard
A1  - Reißel, Martin
A1  - Harlaß, Carsten
T1  - Semi-parametric survival function estimators deduced from an identifying Volterra type integral equation
JF  - Journal of multivariate analysis
N2  - Based on an identifying Volterra type integral equation for randomly right censored observations from a lifetime distribution function F, we solve the corresponding estimating equation by an explicit and implicit Euler scheme. While the first approach results in some known estimators, the second one produces new semi-parametric and pre-smoothed Kaplan–Meier estimators which are real distribution functions rather than sub-distribution functions as the former ones are. This property of the new estimators is particular useful if one wants to estimate the expected lifetime restricted to the support of the observation time.

Specifically, we focus on estimation under the semi-parametric random censorship model (SRCM), that is, a random censorship model where the conditional expectation of the censoring indicator given the observation belongs to a parametric family. We show that some estimated linear functionals which are based on the new semi-parametric estimator are strong consistent, asymptotically normal, and efficient under SRCM. In a small simulation study, the performance of the new estimator is illustrated under moderate sample sizes. Finally, we apply the new estimator to a well-known real dataset.
KW  - Volterra integral equation
KW  - Product-integration
KW  - Asymptotic efficiency
KW  - Semi-parametric random censorship model
KW  - Censored data
KW  - Survival analysis
Y1  - 2016
U6  - http://dx.doi.org/10.1016/j.jmva.2016.02.008
IS  - 147
SP  - 273
EP  - 284
PB  - Elsevier
CY  - Amsterdam
ER  -