Aydın Dursun, Ahmed Syed Ejaz, Yılmaz Ersin
Department of Statistics, Faculty of Science, Mugla Sitki Kocman University, Kotekli 48000, Turkey.
Department of Mathematics and Statistics, Faculty of Science, Brock University, 1812 Sir Isaac Brock Way, St. Catharines, ON L2S 3A1, Canada.
Entropy (Basel). 2021 Nov 27;23(12):1586. doi: 10.3390/e23121586.
This paper focuses on the adaptive spline (A-spline) fitting of the semiparametric regression model to time series data with right-censored observations. Typically, there are two main problems that need to be solved in such a case: dealing with censored data and obtaining a proper A-spline estimator for the components of the semiparametric model. The first problem is traditionally solved by the synthetic data approach based on the Kaplan-Meier estimator. In practice, although the synthetic data technique is one of the most widely used solutions for right-censored observations, the transformed data's structure is distorted, especially for heavily censored datasets, due to the nature of the approach. In this paper, we introduced a modified semiparametric estimator based on the A-spline approach to overcome data irregularity with minimum information loss and to resolve the second problem described above. In addition, the semiparametric B-spline estimator was used as a benchmark method to gauge the success of the A-spline estimator. To this end, a detailed Monte Carlo simulation study and a real data sample were carried out to evaluate the performance of the proposed estimator and to make a practical comparison.
本文聚焦于半参数回归模型的自适应样条（A样条）拟合，以处理带有右删失观测值的时间序列数据。通常，在这种情况下需要解决两个主要问题：处理删失数据以及为半参数模型的分量获得合适的A样条估计量。传统上，第一个问题通过基于Kaplan-Meier估计量的合成数据方法来解决。实际上，尽管合成数据技术是右删失观测值最广泛使用的解决方案之一，但由于该方法的性质，变换后的数据结构会被扭曲，特别是对于高度删失的数据集。在本文中，我们引入了一种基于A样条方法的改进半参数估计量，以最小化信息损失来克服数据不规则性，并解决上述第二个问题。此外，半参数B样条估计量被用作基准方法来衡量A样条估计量的成功程度。为此，进行了详细的蒙特卡罗模拟研究和一个实际数据样本，以评估所提出估计量的性能并进行实际比较。
