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

Dongxiao Han; Jian Huang; Yuanyuan Lin; Guohao Shen

doi:10.1016/j.jeconom.2021.05.006

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

Journal article

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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, Vol.230(2), pp.416-431

2021

DOI: 10.1016/j.jeconom.2021.05.006

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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.

Confidence interval

Huber loss

Linear model

Post-selection inference

Details

Title: Subtitle: Robust post-selection inference of high-dimensional mean regression with heavy-tailed asymmetric or heteroskedastic errors
Creators: Dongxiao Han - Nankai University
Jian Huang - University of Iowa
Yuanyuan Lin - Chinese University of Hong Kong
Guohao Shen - Chinese University of Hong Kong
Resource Type: Journal article
Publication Details: Journal of econometrics, Vol.230(2), pp.416-431
DOI: 10.1016/j.jeconom.2021.05.006
ISSN: 0304-4076
eISSN: 1872-6895
Publisher: Elsevier B.V
Grant note: DOI: 10.13039/100000001, name: National Science Foundation, award: DMS-1916199; DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 11961028; DOI: 10.13039/501100002920, name: Research Grants Council, University Grants Committee, award: 14306219, 14306620; DOI: 10.13039/501100004853, name: Chinese University of Hong Kong; DOI: 10.13039/501100012226, name: Fundamental Research Funds for the Central Universities, award: 9920200110
Language: English
Date published: 2021
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9984257719702771

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