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A New Perspective on High Dimensional Confidence Intervals
Preprint   Open access

A New Perspective on High Dimensional Confidence Intervals

Logan Harris and Patrick Breheny
ArXiv.org
Cornell University
08/05/2025
DOI: 10.48550/arxiv.2508.03504
url
https://arxiv.org/abs/2508.03504v1View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Classically, confidence intervals are required to have consistent coverage across all values of the parameter. However, this will inevitably break down if the underlying estimation procedure is biased. For this reason, many efforts have focused on debiased versions of the lasso for interval construction. In the process of debiasing, however, the connection to the original estimates are often obscured. In this work, we offer a different perspective focused on average coverage in contrast to individual coverage. This perspective results in confidence intervals that better reflect the original assumptions, as opposed to debiased intervals, which often do not even contain the original lasso estimates. To this end we propose a method based on the Relaxed Lasso that gives approximately correct average coverage and compare this to debiased methods which attempt to produce correct individual coverage. With this new definition of coverage we also briefly revisit the bootstrap, which Chatterjee and Lahiri (2010) showed was inconsistent for lasso, but find that it fails even under this alternative coverage definition.
 Statistics - Methodology

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