Yılmaz Ersin, Aydın Dursun, Ahmed S Ejaz
Department of Statistics, Mugla Sıtkı Kocman University, Mugla 48000, Turkey.
Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada.
Entropy (Basel). 2023 Sep 7;25(9):1307. doi: 10.3390/e25091307.
This paper introduces a modified local linear estimator (LLR) for partially linear additive models (PLAM) when the response variable is subject to random right-censoring. In the case of modeling right-censored data, PLAM offers a more flexible and realistic approach to the estimation procedure by involving multiple parametric and nonparametric components. This differs from the widely used partially linear models that feature a univariate nonparametric function. The LLR method is employed to estimate unknown smooth functions using a modified backfitting algorithm, delivering a non-iterative solution for the right-censored PLAM. To address the censorship issue, three approaches are employed: synthetic data transformation (ST), Kaplan-Meier weights (KMW), and the kNN imputation technique (kNNI). Asymptotic properties of the modified backfitting estimators are detailed for both ST and KMW solutions. The advantages and disadvantages of these methods are discussed both theoretically and practically. Comprehensive simulation studies and real-world data examples are conducted to assess the performance of the introduced estimators. The results indicate that LLR performs well with both KMW and kNNI in the majority of scenarios, along with a real data example.
本文介绍了一种用于部分线性可加模型（PLAM）的修正局部线性估计器（LLR），该模型中的响应变量受到随机右删失的影响。在对右删失数据进行建模时，PLAM通过纳入多个参数和非参数成分，为估计过程提供了一种更灵活、更现实的方法。这与广泛使用的具有单变量非参数函数的部分线性模型不同。LLR方法用于使用修正的反向拟合算法估计未知的光滑函数，为右删失的PLAM提供了一种非迭代的解决方案。为了解决删失问题，采用了三种方法：合成数据变换（ST）、Kaplan-Meier权重（KMW）和k近邻插补技术（kNNI）。详细阐述了修正的反向拟合估计器对于ST和KMW解决方案的渐近性质。从理论和实际两方面讨论了这些方法的优缺点。进行了全面的模拟研究和实际数据示例，以评估所引入估计器的性能。结果表明，在大多数情况下，LLR与KMW和kNNI都表现良好，同时还给出了一个实际数据示例。
