Berg Arthur, Politis Dimitris, Suaray Kagba, Zeng Hui
Penn State College of Medicine, Division of Biostatistics & Bioinformatics.
University of California, San Diego, Department of Mathematics.
Test (Madr). 2020 Sep;29(3):704-727. doi: 10.1007/s11749-019-00677-z. Epub 2019 Aug 17.
Kernel-based nonparametric hazard rate estimation is considered with a special class of infinite-order kernels that achieves favorable bias and mean square error properties. A fully automatic and adaptive implementation of a density and hazard rate estimator is proposed for randomly right censored data. Careful selection of the bandwidth in the proposed estimators yields estimates that are more efficient in terms of overall mean squared error performance, and in some cases achieves a nearly parametric convergence rate. Additionally, rapidly converging bandwidth estimates are presented for use in second-order kernels to supplement such kernel-based methods in hazard rate estimation. Simulations illustrate the improved accuracy of the proposed estimator against other nonparametric estimators of the density and hazard function. A real data application is also presented on survival data from 13,166 breast carcinoma patients.
基于核的非参数危险率估计是针对一类特殊的无穷阶核进行考虑的，这类核具有良好的偏差和均方误差性质。针对随机右删失数据，提出了一种密度和危险率估计器的全自动自适应实现方法。在所提出的估计器中仔细选择带宽，可得到在整体均方误差性能方面更有效的估计，并且在某些情况下实现了近乎参数收敛速率。此外，还给出了用于二阶核的快速收敛带宽估计，以补充危险率估计中此类基于核的方法。模拟结果表明，与密度和危险函数的其他非参数估计器相比，所提出的估计器具有更高的精度。还给出了一个关于13166例乳腺癌患者生存数据的实际应用。
