Balanced estimation for high-dimensional measurement error models
Balanced estimation for high-dimensional measurement error models
复制标题
高维测量误差模型的平衡估计
DOI：
10.1016/j.csda.2018.04.009
复制
发表时间：
2018
影响因子：
1.8
通讯作者：
Li Gaorong
中科院分区：
文献类型：
--
作者：
Zheng Zemin;Li Yang;Yu Chongxiu;Li Gaorong
在真实的应用中经常会遇到噪声和缺失数据，使得观测到的协变量包含测量误差。尽管在高维中污染协变量的模型选择取得了快速进展，但在预测，变量选择和计算的各个方面都享有优势的方法仍然在很大程度上未被探索。在本文中，我们提出了一种新的方法称为平衡估计的高维误差的变量回归，以实现一个理想的平衡之间的预测和变量选择的加性和乘性的测量误差。它结合了最近半正定投影和组合L-1和凹正则化的优点，因此可以通过坐标优化算法有效地求解。我们还提供了理论上的保证，所提出的方法，通过建立预言预测和估计误差界相当于那些Lasso与干净的数据集，以及一个明确的和渐近消失的假符号率，控制过度拟合，测量误差下的一个严重问题的界限。我们的数值研究表明，变量选择的改进将反过来提高预测和估计性能下的测量误差。(C)2018爱思唯尔B. V.保留所有权利。
Noisy and missing data are often encountered in real applications such that the observed covariates contain measurement errors. Despite the rapid progress of model selection with contaminated covariates in high dimensions, methodology that enjoys virtues in all aspects of prediction, variable selection, and computation remains largely unexplored. In this paper, we propose a new method called as the balanced estimation for high-dimensional error-in-variables regression to achieve an ideal balance between prediction and variable selection under both additive and multiplicative measurement errors. It combines the strengths of the nearest positive semi-definite projection and the combined L-1 and concave regularization, and thus can be efficiently solved through the coordinate optimization algorithm. We also provide theoretical guarantees for the proposed methodology by establishing the oracle prediction and estimation error bounds equivalent to those for Lasso with the clean data set, as well as an explicit and asymptotically vanishing bound on the false sign rate that controls overfitting, a serious problem under measurement errors. Our numerical studies show that the amelioration of variable selection will in turn improve the prediction and estimation performance under measurement errors. (C) 2018 Elsevier B.V. All rights reserved.