A Wald-type variance estimation for the nonparametric distribution estimators for doubly censored data
A Wald-type variance estimation for the nonparametric distribution estimators for doubly censored data
复制标题
双删失数据非参数分布估计的 Wald 型方差估计
DOI：
10.1007/s10463-009-0251-3
复制
发表时间：
2011
影响因子：
1
通讯作者：
T
中科院分区：
文献类型：
--
作者：
Sugimoto;T
讨论了双截尾数据的非参数分布估计量的方差估计。我们首先提供了构建剖面似然的Kuhn-Tucker条件的另一种观点，并提出了一种与EM算法不同的Newton-Raphson算法作为优化技术。主要提出了一种基于微分条件链式法则的无迭代wald型方差估计来构造轮廓似然，该方法将方差公式推广到只有左截或右截的数据中。在这个估计过程中，我们克服了直接将特恩布尔公式应用于大样本所带来的一些困难，避免了求解Fredholm方程、计算轮廓似然比或使用bootstrap等计算量大的迭代负荷。此外，我们还建立了公式wald型方差估计量的相合性。此外，还进行了模拟研究，以研究有限样本中wald型方差估计的性质，并将其与来自剖面似然比的估计进行比较。
We discuss the variance estimation for the nonparametric distribution estimator for doubly censored data. We first provide another view of Kuhn–Tucker’s conditions to construct the profile likelihood, and lead a Newton–Raphson algorithm as an optimization technique unlike the EM algorithm. The main proposal is an iteration-free Wald-type variance estimate based on the chain rule of differentiating conditions to construct the profile likelihood, which generalizes the variance formula in only right- or left-censored data. In this estimation procedure, we overcome some difficulties caused in directly applying Turnbull’s formula to large samples and avoid a load with computationally heavy iterations, such as solving the Fredholm equations, computing the profile likelihood ratio or using the bootstrap. Also, we establish the consistency of the formulated Wald-type variance estimator. In addition, simulation studies are performed to investigate the properties of the Wald-type variance estimates in finite samples in comparison with those from the profile likelihood ratio.