A2065
Title: Rank-based sparse regression in principal components space under measurement error
Authors: Long Feng - Nankai University (China)
Xiaoyi Wang - Beijing Normal University at Zhuhai (China)
Le Zhou - Hong Kong Baptist University (Hong Kong)
Xiaoyi Wang - Beijing Normal University at Zhuhai (China) [presenting]
Abstract: High-dimensional regression in principal components space is studied when the predictors are observed with measurement error and the response errors may be heavy-tailed. A penalized rank-based pilot estimator in the principal component space is first proposed and its prediction error is analyzed. The prediction error consists of a term with the minimax rate plus an additional term representing the impact of measurement error which diminishes as the dimension grows. The error distribution is not required to have any finite moment in the theory, and the pilot estimator therefore enjoys the blessings-of-dimensionality property in heavy-tailed measurement error regression. To further reduce bias, an adaptively reweighted second stage rank estimator is then proposed and its strong oracle property is established. In particular, the second stage estimator is capable of improving the prediction error to the oracle rate corresponding to the active set of principal components. Simulation studies demonstrate that the proposed method remains competitive under light-tailed errors and is substantially more efficient under heavy-tailed errors, especially when predictor contamination is present. A real data example is analyzed to demonstrate the application of the method.
