TY  - JOUR
A1  - Dikta, Gerhard
T1  - Asymptotically efficient estimation under semi-parametric random censorship models
JF  - Journal of multivariate analysis
N2  - We study the estimation of some linear functionals which are based on an unknown lifetime distribution. The observations are assumed to be generated 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. Under this setup a semi-parametric estimator of the survival function was introduced by the author. If the parametric model assumption is correct, it is known that the estimated functional which is based on this semi-parametric estimator is asymptotically at least as efficient as the corresponding one which rests on the nonparametric Kaplan–Meier estimator.

In this paper we show that the estimated functional which is based on this semi-parametric estimator is asymptotically efficient with respect to the class of all regular estimators under this semi-parametric model.
Y1  - 2014
U6  - http://dx.doi.org/10.1016/j.jmva.2013.10.002
SN  - 1095-7243 (E-Journal); 0047-259X (Print)
VL  - 124
SP  - 10
EP  - 24
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Dikta, Gerhard
A1  - Kühlheim, René
A1  - Mendonca, Jorge
A1  - Una-Alcarez, Jacobo de
T1  - Asymptotic representation of presmoothed Kaplan–Meier integrals with covariates in a semiparametric censorship model
JF  - Journal of Statistical Planning and Inference
Y1  - 2015
U6  - http://dx.doi.org/10.1016/j.jspi.2015.12.001
SN  - 0378-3758
VL  - Vol. 171
SP  - 10
EP  - 37
PB  - Elsevier
CY  - Amsterdam
ER  - 
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  - 
TY  - JOUR
A1  - Dikta, Gerhard
T1  - Semi-parametric random censorship models
JF  - From Statistics to Mathematical Finance : Festschrift in Honour of Winfried Stute
Y1  - 2017
SN  - 978-3-319-50986-0
U6  - http://dx.doi.org/10.1007/978-3-319-50986-0_3
SP  - 43
EP  - 56
PB  - Springer
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Heel, Mareike van
A1  - Dikta, Gerhard
A1  - Braekers, Roel
T1  - Bootstrap based goodness‑of‑fit tests for binary multivariate regression models
JF  - Journal of the Korean Statistical Society
N2  - We consider a binary multivariate regression model where the conditional expectation of a binary variable given a higher-dimensional input variable belongs to a parametric family. Based on this, we introduce a model-based bootstrap (MBB) for higher-dimensional input variables. This test can be used to check whether a sequence of independent and identically distributed observations belongs to such a parametric family. The approach is based on the empirical residual process introduced by Stute (Ann Statist 25:613–641, 1997). In contrast to Stute and Zhu’s approach (2002) Stute & Zhu (Scandinavian J Statist 29:535–545, 2002), a transformation is not required. Thus, any problems associated with non-parametric regression estimation are avoided. As a result, the MBB method is much easier for users to implement. To illustrate the power of the MBB based tests, a small simulation study is performed. Compared to the approach of Stute & Zhu (Scandinavian J Statist 29:535–545, 2002), the simulations indicate a slightly improved power of the MBB based method. Finally, both methods are applied to a real data set.
Y1  - 2021
U6  - http://dx.doi.org/10.1007/s42952-021-00142-4
SN  - 2005-2863 (Online)
SN  - 1226-3192 (Print)
N1  - Corresponding author: Mareike van Heel
VL  - 51
PB  - Springer Nature
CY  - Singapur
ER  -