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Double bias correction for high-dimensional sparse additive hazards regression with covariate measurement errors
Lifetime Data Analysis ( IF 1.3 ) Pub Date : 2022-07-22 , DOI: 10.1007/s10985-022-09568-2
Xiaobo Wang 1 , Jiayu Huang 1 , Guosheng Yin 2 , Jian Huang 3 , Yuanshan Wu 4
Affiliation  

We propose an inferential procedure for additive hazards regression with high-dimensional survival data, where the covariates are prone to measurement errors. We develop a double bias correction method by first correcting the bias arising from measurement errors in covariates through an estimating function for the regression parameter. By adopting the convex relaxation technique, a regularized estimator for the regression parameter is obtained by elaborately designing a feasible loss based on the estimating function, which is solved via linear programming. Using the Neyman orthogonality, we propose an asymptotically unbiased estimator which further corrects the bias caused by the convex relaxation and regularization. We derive the convergence rate of the proposed estimator and establish the asymptotic normality for the low-dimensional parameter estimator and the linear combination thereof, accompanied with a consistent estimator for the variance. Numerical experiments are carried out on both simulated and real datasets to demonstrate the promising performance of the proposed double bias correction method.



中文翻译:

具有协变量测量误差的高维稀疏加性风险回归的双偏差校正

我们提出了一种使用高维生存数据进行加性风险回归的推理程序,其中协变量容易出现测量误差。我们开发了一种双偏差校正方法,首先通过回归参数的估计函数校正协变量中测量误差引起的偏差。采用凸松弛技术,在估计函数的基础上精心设计可行损失,得到回归参数的正则化估计量,并通过线性规划求解。使用 Neyman 正交性,我们提出了一个渐进无偏估计器,它进一步纠正了由凸松弛和正则化引起的偏差。我们推导了所提出的估计器的收敛速度,并为低维参数估计器及其线性组合建立了渐​​近正态性,并附有一致的方差估计器。对模拟和真实数据集进行了数值实验,以证明所提出的双偏差校正方法的良好性能。

更新日期:2022-07-24
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