Regression Analysis of Doubly Truncated Data
Regression Analysis of Doubly Truncated Data
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DOI：
10.1080/01621459.2019.1585252
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发表时间：
2017-01
影响因子：
3.7
通讯作者：
Z. Ying;Wen Yu;Ziqiang Zhao;M. Zheng
中科院分区：
文献类型：
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作者：
Z. Ying;Wen Yu;Ziqiang Zhao;M. Zheng
摘要在天文学、计量经济学和生存分析文献中发现了双截断数据。当每一次观察都被限制在一个区间内时，也就是说，只有那些落在它们各自区间内的观察才能沿着这些区间被观察到。与基于计数过程的方法可以处理的单侧截断不同，双重截断数据更难以处理。在他们对天文数据集的分析中，Efron和Petrosian提出了一些双截断数据的非参数方法。受他们的方法以及Bhattacharya等人对右截断数据的工作的启发，我们提出了一种估计因变量受双重截断影响时回归参数的一般方法。它扩展了Mann-Whitney型秩估计，并且可以通过现有的软件包轻松计算。加权秩估计也被认为是提高估计效率。我们证明了所得到的估计是一致的和渐近正态的。为了逼近极限分布，提出了具有大样本合理性的恢复方案。用新方法分析了Efron和Petrosian的类星体数据以及AIDS的孵化数据。仿真结果表明，该方法具有较好的性能.
Abstract Doubly truncated data are found in astronomy, econometrics, and survival analysis literature. They arise when each observation is confined to an interval, that is, only those which fall within their respective intervals are observed along with the intervals. Unlike the one-sided truncation that can be handled by counting process-based approach, doubly truncated data are much more difficult to handle. In their analysis of an astronomical dataset, Efron and Petrosian proposed some nonparametric methods for doubly truncated data. Motivated by their approach, as well as by the work of Bhattacharya et al. for right truncated data, we propose a general method for estimating the regression parameter when the dependent variable is subject to the double truncation. It extends the Mann–Whitney-type rank estimator and can be computed easily by existing software packages. Weighted rank estimation is also considered for improving estimation efficiency. We show that the resulting estimators are consistent and asymptotically normal. Resampling schemes are proposed with large sample justification for approximating the limiting distributions. The quasar data in Efron and Petrosian and an AIDS incubation data are analyzed by the new method. Simulation results show that the proposed method works well.