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Semi-parametric random censorship models. (English) Zbl 1383.62211
Ferger, Dietmar (ed.) et al., From statistics to mathematical finance. Festschrift in honour of Winfried Stute. Cham: Springer (ISBN 978-3-319-50985-3/hbk; 978-3-319-50986-0/ebook). 43-56 (2017).
Summary: Starting with an identifying Volterra type integral equation for the survival function under randomly right censored observations, we derive general product type estimators. These general estimators can be specified according to the additional information about the conditional expectation of the indicator given the observation time. Among others, the well-known nonparametric Kaplan-Meier and two semi-parametric estimators are derived. For the latter ones, the conditional expectation of the indicator has to be parameterizable. Some important probabilistic properties of these semi-parametric estimators are reviewed here together with their nonparametric counterparts. In particular, a strong law and asymptotic normality of semi-parametric integrals together with their efficiency are discussed. Furthermore, validation tests for the parametric assumption are considered and bootstrapping under these semi-parametric models is reviewed.
For the entire collection see [Zbl 1383.62010].
MSC:
62N01 Censored data models
62N02 Estimation in survival analysis and censored data
62G05 Nonparametric estimation
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