Confidence Intervals for Linear Models with Arbitrary Noise Contamination

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ID: 330070
2026
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Abstract
Summary We study confidence interval construction for linear regression under Huber’s contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood, statistical inference remains challenging, especially because the contamination proportion is not identifiable from the data. We develop a new algorithm that constructs confidence intervals for individual regression coefficients without any prior knowledge of the contamination level. Our method is based on a Z-estimation framework using a smooth estimating function. The method directly quantifies the uncertainty of the estimating equation after a pre-processing step that decorrelates covariates associated with the nuisance parameters. We show that the resulting confidence interval has valid coverage uniformly over all contamination distributions and attains an optimal length of order O(1n(1−ϵ)2), matching the rate achievable when the contamination proportion ϵ is known. This result stands in sharp contrast to the adaptation cost of robust interval estimation observed in the simpler Gaussian location model.
Reference Key
openalex_W4416189291 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Dong Xie, Gao Chao, John Lafferty
Journal jurnal biometrika dan kependudukan
Year 2026
DOI
10.1093/biomet/asag058
URL
https://doi.org/10.1093/biomet/asag058
Keywords Keywords not found

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