Emura Takeshi, Konno Yoshihiko, Michimae Hirofumi
Graduate Institute of Statistics, National Central University, Zhongli, Taiwan,
Lifetime Data Anal. 2015 Jul;21(3):397-418. doi: 10.1007/s10985-014-9297-5. Epub 2014 Jul 8.
Doubly truncated data consist of samples whose observed values fall between the right- and left- truncation limits. With such samples, the distribution function of interest is estimated using the nonparametric maximum likelihood estimator (NPMLE) that is obtained through a self-consistency algorithm. Owing to the complicated asymptotic distribution of the NPMLE, the bootstrap method has been suggested for statistical inference. This paper proposes a closed-form estimator for the asymptotic covariance function of the NPMLE, which is computationally attractive alternative to bootstrapping. Furthermore, we develop various statistical inference procedures, such as confidence interval, goodness-of-fit tests, and confidence bands to demonstrate the usefulness of the proposed covariance estimator. Simulations are performed to compare the proposed method with both the bootstrap and jackknife methods. The methods are illustrated using the childhood cancer dataset.
双截断数据由观测值落在左右截断限之间的样本组成。对于此类样本，使用通过自一致性算法获得的非参数最大似然估计器（NPMLE）来估计感兴趣的分布函数。由于NPMLE的渐近分布复杂，已建议使用自助法进行统计推断。本文提出了一种NPMLE渐近协方差函数的闭式估计器，它是一种在计算上比自助法更具吸引力的替代方法。此外，我们开发了各种统计推断程序，如置信区间、拟合优度检验和置信带，以证明所提出的协方差估计器的有用性。进行模拟以将所提出的方法与自助法和刀切法进行比较。使用儿童癌症数据集对这些方法进行了说明。
