Automatic bias correction for testing in high‐dimensional linear models

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Zhou, Jing ORCID: https://orcid.org/0000-0002-8894-9100 and Claeskens, Gerda (2023) Automatic bias correction for testing in high‐dimensional linear models. Statistica Neerlandica, 77 (1). pp. 71-98. ISSN 1467-9574

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Abstract

Hypothesis testing is challenging due to the test statistic's complicated asymptotic distribution when it is based on a regularized estimator in high dimensions. We propose a robust testing framework for l1-regularized M-estimators to cope with non-Gaussian distributed regression errors, using the robust approximate message passing algorithm. The proposed framework enjoys an automatically built-in bias correction and is applicable with general convex nondifferentiable loss functions which also allows inference when the focus is a conditional quantile instead of the mean of the response. The estimator compares numerically well with the debiased and desparsified approaches while using the least squares loss function. The use of the Huber loss function demonstrates that the proposed construction provides stable confidence intervals under different regression error distributions.

Item Type: Article
Additional Information: Funding information: Fonds Wetenschappelijk Onderzoek Junior Postdoc Fellowship, KU Leuven Research Fund, Grant/Award Number: C16/20/002
Uncontrolled Keywords: approximate message passing algorithm,confidence interval,high-dimensional linear model,hypothesis testing,loss function,ℓ -regularization,statistics and probability,statistics, probability and uncertainty ,/dk/atira/pure/subjectarea/asjc/2600/2613
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Statistics
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Depositing User: LivePure Connector
Date Deposited: 20 Feb 2023 16:30
Last Modified: 02 Dec 2023 03:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/91213
DOI: 10.1111/stan.12274

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