英文文献：Local Linear Density Estimation for Filtered Survival Data, with Bias Correction-局部线性密度估计滤波生存数据，与偏差校正
英文文献作者：Jens Perch Nielsen,Carsten Tanggaard,M.C. Jones
英文文献摘要：
A class of local linear kernel density estimators based on weighted least squares kernel estimation is considered within the framework of Aalen’s multiplicative intensity model. This model includes the filtered data model that, in turn, allows for truncation and/or censoring in addition to accommodat- ing unusual patterns of exposure as well as occurrence. It is shown that the local linear estimators corresponding to all different weightings have the same pointwise asymptotic properties. However, the weighting previously used in the literature in the i.i.d. case is seen to be far from optimal when it comes to exposure robustness, and a simple alternative weighting is to be preferred. Indeed, this weighting has, effectively, to be well chosen in a ‘pilot’ estimator of the survival function as well as in the main estimator itself. We also investigate multiplicative and additive bias correction methods within our framework. The multiplicative bias correction method proves to be best in a simulation study comparing the performance of the considered estimators. An example concerning old age mortality demonstrates the importance of the improvements provided.

摘要在Aalen乘性强度模型的框架下，研究了一类基于加权最小二乘核估计的局部线性核密度估计。该模型包括过滤后的数据模型，该模型除了适应不寻常的暴露模式和发生情况外，还允许截断和/或审查。证明了不同权值对应的局部线性估计具有相同的点态渐近性质。然而，当涉及到暴露稳健性时，文献中先前在i.i.d.案例中使用的权重被认为远远不是最佳的，一个简单的替代权重是首选的。实际上，在生存函数的“先导”估计器中以及在主估计器本身中，都需要有效地选择这种加权。我们也在我们的框架内调查乘法和加法偏差校正方法。在比较估计量性能的仿真研究中，乘法偏差校正方法被证明是最好的。关于老年死亡率的一个例子说明了所提供改善的重要性。