|主题：||Balanced Estimation for High-dimensional Measurement Error Models|
报告题目：Balanced Estimation for High-dimensional Measurement Error Models
报 告 人：李高荣教授（北京工业大学）
Noisy and missing data are oftenencountered in real applications such that the observed covariates containmeasurement errors. Despite the rapid progress of model selection withcontaminated covariates in high dimensions, methodology that enjoys virtues inall aspects of prediction, variable selection, and computation remains largelyunexplored. In this paper, we propose a new method called as the balancedestimation for high-dimensional error-in-variables regression to achieve anideal balance between prediction and variable selection under both additive andmultiplicative measurement errors. It combines the strengths of the nearestpositive semi-definite projection and the combined $L_1$ and concaveregularization, and thus can be efficiently solved through the coordinateoptimization algorithm. We also provide theoretical guarantees for the proposedmethodology by establishing the oracle prediction and estimation error boundsequivalent to those for Lasso with the clean data set, as well as an explicit andasymptotically vanishing bound on the false sign rate that controlsoverfitting, a serious problem under measurement errors. Our numerical studiesshow that the amelioration of variable selection will in turn improve theprediction and estimation performance under measurement errors.