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A robust variable screening method for high-dimensional data

Tao Wang, Lin Zheng, Zhonghua Li and Haiyang Liu

Journal of Applied Statistics, 2017, vol. 44, issue 10, 1839-1855

Abstract: In practice, the presence of influential observations may lead to misleading results in variable screening problems. We, therefore, propose a robust variable screening procedure for high-dimensional data analysis in this paper. Our method consists of two steps. The first step is to define a new high-dimensional influence measure and propose a novel influence diagnostic procedure to remove those unusual observations. The second step is to utilize the sure independence screening procedure based on distance correlation to select important variables in high-dimensional regression analysis. The new influence measure and diagnostic procedure that we developed are model free. To confirm the effectiveness of the proposed method, we conduct simulation studies and a real-life data analysis to illustrate the merits of the proposed approach over some competing methods. Both the simulation results and the real-life data analysis demonstrate that the proposed method can greatly control the adverse effect after detecting and removing those unusual observations, and performs better than the competing methods.

Date: 2017
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DOI: 10.1080/02664763.2016.1238044

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