Asymptotic distribution of the nonparametric distribution estimator based on a martingale approach in doubly censored data
Asymptotic distribution of the nonparametric distribution estimator based on a martingale approach in doubly censored data
复制标题
双删失数据中基于鞅方法的非参数分布估计量的渐近分布
DOI：
10.1007/s10463-012-0395-4
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发表时间：
2013
影响因子：
1
通讯作者：
T
中科院分区：
文献类型：
--
作者：
Sugimoto;T
对于不完全信息的事件时间数据的分析，提出了许多关于分布推理和回归模型的推广。然而，鞅方法在这一领域的发展并没有取得很大进展，而对于右删减数据，这种方法已经广泛应用于研究估计量的渐近性质和推导回归诊断方法。本文以双截尾数据为研究对象，讨论了非参数极大似然估计的鞅推理方法。我们使用半参数轮廓似然的分数函数来构造NPMLE的鞅结构。最后，在不依赖于无穷矩阵表达式的情况下，更方便地导出了NPMLE的渐近分布表达式。进一步有用的一点是，NPMLE的方差-协方差公式可以在更大的样本中计算，作为这里给出的极限形式的经验版本。
For analysis of time-to-event data with incomplete information beyond right-censoring, many generalizations of the inference of the distribution and regression model have been proposed. However, the development of martingale approaches in this area has not progressed greatly, while for right-censored data such an approach has spread widely to study the asymptotic properties of estimators and to derive regression diagnosis methods. In this paper, focusing on doubly censored data, we discuss a martingale approach for inference of the nonparametric maximum likelihood estimator (NPMLE). We formulate a martingale structure of the NPMLE using a score function of the semiparametric profile likelihood. Finally, an expression of the asymptotic distribution of the NPMLE is derived more conveniently without depending on an infinite matrix expression as in previous research. A further useful point is that a variance-covariance formula of the NPMLE computable in a larger sample is obtained as an empirical version of the limit form presented here.