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2019 Variable selection via adaptive false negative control in linear regression
X. Jessie Jeng, Xiongzhi Chen
Electron. J. Statist. 13(2): 5306-5333 (2019). DOI: 10.1214/19-EJS1649


Variable selection methods have been developed in linear regression to provide sparse solutions. Recent studies have focused on further interpretations on the sparse solutions in terms of false positive control. In this paper, we consider false negative control for variable selection with the goal to efficiently select a high proportion of relevant predictors. Different from existing studies in power analysis and sure screening, we propose to directly estimate the false negative proportion (FNP) of a decision rule and select the smallest subset of predictors that has the estimated FNP less than a user-specified control level. The proposed method is adaptive to the user-specified control level on FNP by selecting less candidates if a higher level is implemented. On the other hand, when data has stronger effect size or larger sample size, the proposed method controls FNP more efficiently with less false positives. New analytic techniques are developed to cope with the major challenge of FNP control when relevant predictors cannot be consistently separated from irrelevant ones. Our numerical results are in line with the theoretical findings.


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X. Jessie Jeng. Xiongzhi Chen. "Variable selection via adaptive false negative control in linear regression." Electron. J. Statist. 13 (2) 5306 - 5333, 2019.


Received: 1 August 2019; Published: 2019
First available in Project Euclid: 17 December 2019

zbMATH: 07147377
MathSciNet: MR4043074
Digital Object Identifier: 10.1214/19-EJS1649

Primary: 62J07
Secondary: 62F03

Keywords: debiased Lasso , FNC-Reg , Post-selection inference , variable screening


Vol.13 • No. 2 • 2019
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