On Estimation of Partially Linear Transformation Models
On Estimation of Partially Linear Transformation Models
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DOI：
10.1198/jasa.2010.tm09302
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发表时间：
2010-06-01
影响因子：
3.7
通讯作者：
Zhang, Hao Helen
中科院分区：
文献类型：
--
作者：
Lu, Wenbin;Zhang, Hao Helen
我们研究了一类一般的部分线性变换模型，它通过在生存数据分析中引入非线性协变量效应来扩展线性变换模型。为了统一估计参数和非参数协变量效应，提出了一种新的估计方程方法，该方法由全局估计方程和核加权局部估计方程组成。我们证明了在适当选择核带宽参数的情况下，线性效应的参数估计是一致的和渐近正态的。还建立了估计的非线性效应的渐近性质。我们进一步提出了一种简单的重采样方法来估计线性估计的渐近方差，并证明了其有效性。为了便于新方法的实施，提出了一种迭代算法。给出了数值算例，说明了该方法在有限样本下的性能。补充材料可以在网上找到。
We study a general class of partially linear transformation models, which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis. A new martingale-based estimating equation approach, consisting of both global and kernel-weighted local estimation equations, is developed for estimating the parametric and nonparametric covariate effects in a unified manner. We show that with a proper choice of the kernel bandwidth parameter, one can obtain the consistent and asymptotically normal parameter estimates for the linear effects. Asymptotic properties of the estimated nonlinear effects are established as well. We further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness. To facilitate the implementation of the new procedure, an iterative algorithm is developed. Numerical examples are given to illustrate the finite-sample performance of the procedure. Supplementary materials are available online.