Robust post-selection inference of high-dimensional mean regression with heavy-tailed asymmetric or heteroskedastic errors

Dongxiao Han, Jian Huang, Yuanyuan Lin and Guohao Shen

Journal of Econometrics, 2022, vol. 230, issue 2, 416-431

Abstract: We propose a robust post-selection inference method based on the Huber loss for the regression coefficients, when the error distribution is heavy-tailed and asymmetric in a high-dimensional linear model with an intercept term. The asymptotic properties of the resulting estimators are established under mild conditions. We also extend the proposed method to accommodate heteroscedasticity assuming the error terms are symmetric and other suitable conditions. Statistical tests for low-dimensional parameters or individual coefficient in the high-dimensional linear model are also studied. Simulation studies demonstrate desirable properties of the proposed method. An application to a genomic dataset about riboflavin production rate is provided.

Keywords: Confidence interval; Huber loss; Linear model; Post-selection inference (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:230:y:2022:i:2:p:416-431

DOI: 10.1016/j.jeconom.2021.05.006

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