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Estimation from cross-sectional data under a semiparametric truncation model
Biometrika ( IF 2.7 ) Pub Date : 2020-04-11 , DOI: 10.1093/biomet/asaa002 C Heuchenne 1 , J De Uña-Álvarez 2 , G Laurent 1
Biometrika ( IF 2.7 ) Pub Date : 2020-04-11 , DOI: 10.1093/biomet/asaa002 C Heuchenne 1 , J De Uña-Álvarez 2 , G Laurent 1
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Cross-sectional sampling is often used when investigating inter-event times, resulting in left-truncated and right-censored data. In this paper, we consider a semiparametric truncation model in which the truncating variable is assumed to belong to a certain parametric family. We examine two methods of estimating both the truncation and the lifetime distributions. We obtain asymptotic representations of the estimators for the lifetime distribution and establish their weak convergence. Both of the proposed estimators perform better than Wang’s (1991) nonparametric maximum likelihood estimator in terms of the integrated mean squared error, when the parametric family for the truncation is sufficiently close to its true distribution. The full likelihood approach is preferable to the conditional likelihood approach in estimating the lifetime distribution, though not necessarily the truncation distribution. In an application to Alzheimer’s disease data, hypothesis tests reject the uniform truncation distribution, but several other parametric models lead to similar behaviour of the truncation and lifetime distributions after disease onset.
中文翻译:
在半参数截断模型下根据横截面数据进行估算
在调查事件间时间时,经常使用横截面采样,从而产生左截断和右删截的数据。在本文中,我们考虑一个半参数截断模型,其中假定截断变量属于某个参数族。我们研究了两种估计截断和生存期分布的方法。我们获得了寿命分布估计量的渐近表示,并建立了它们的弱收敛性。当截断的参数族足够接近其真实分布时,两个建议的估计器在积分均方误差方面都比Wang(1991)的非参数最大似然估计器更好。在估计寿命分布时,全似然法优于条件似然法,尽管不一定要截断分布。在对阿尔茨海默氏病数据的应用中,假设检验拒绝了统一的截短分布,但是其他几种参数模型也导致了疾病发作后截短的行为和寿命分布。
更新日期:2020-04-11
中文翻译:
在半参数截断模型下根据横截面数据进行估算
在调查事件间时间时,经常使用横截面采样,从而产生左截断和右删截的数据。在本文中,我们考虑一个半参数截断模型,其中假定截断变量属于某个参数族。我们研究了两种估计截断和生存期分布的方法。我们获得了寿命分布估计量的渐近表示,并建立了它们的弱收敛性。当截断的参数族足够接近其真实分布时,两个建议的估计器在积分均方误差方面都比Wang(1991)的非参数最大似然估计器更好。在估计寿命分布时,全似然法优于条件似然法,尽管不一定要截断分布。在对阿尔茨海默氏病数据的应用中,假设检验拒绝了统一的截短分布,但是其他几种参数模型也导致了疾病发作后截短的行为和寿命分布。