Semi-parametric survival function estimators deduced from an identifying Volterra type integral equation

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• 作者：Gerhard Dikta^a ; ^{dikta@fh-aachen.de" class="auth_mail" title="E-mail the corresponding author} ; Martin Reiß ; el^a ; ^{reissel@fh-aachen.de" class="auth_mail" title="E-mail the corresponding author} ; Carsten Harlaß ; ^a ; ^b ; ^{charlass@uwm.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：62N01 ; 62N02 ; 62E20
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：147
• 期：Complete
• 页码：273-284
• 全文大小：397 K

文摘

Based on an identifying Volterra type integral equation for randomly right censored observations from a lifetime distribution function 62cfc1054697e6e382b1d0ddd" title="Click to view the MathML source">F$F$, 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.