Honest Inference for High-Dimensional Linear Models
Abstract
We propose a heteroskedasticity-robust and dimention-adaptive test for multiple linear restric- tions in sparse high-dimensional linear regression models. It combines desparsified LASSO estimation with a ridge-regularized quadratic form statistic and critical values that adapt to the restriction dimension. Under stated regularity conditions, our approach is asymptotically valid under a fixed or diverging number of restrictions without specifying the asymptotic regime in advance. Our random-design theory allows independent non-identically distributed covari- ate rows with marginal sub-Weibull tails and heteroskedastic errors satisfying finite polynomial moments. Monte Carlo simulations demonstrate improved finite-sample size control relative to conventional Wald tests, particularly as the number of restrictions increases.
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BibTeX
@misc{lim2026honest,
title = {{Honest Inference for High-Dimensional Linear Models}},
author = {Dennis Lim and Pengjin Min and Jonathan H. W. Tan and Jiezheng Wei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16503},
eprint = {2610.16503},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16503},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Honest Inference for High-Dimensional Linear Models
AU - Dennis Lim
AU - Pengjin Min
AU - Jonathan H. W. Tan
AU - Jiezheng Wei
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16503
UR - https://arxiv.org/abs/2610.16503
AB - We propose a heteroskedasticity-robust and dimention-adaptive test for multiple linear restric- tions in sparse high-dimensional linear regression models. It combines desparsified LASSO estimation with a ridge-regularized quadratic form statistic and critical values that adapt to the restriction dimension. Under stated regularity conditions, our approach is asymptotically valid under a fixed or diverging number of restrictions without specifying the asymptotic regime in advance. Our random-design theory allows independent non-identically distributed covari- ate rows with marginal sub-Weibull tails and heteroskedastic errors satisfying finite polynomial moments. Monte Carlo simulations demonstrate improved finite-sample size control relative to conventional Wald tests, particularly as the number of restrictions increases.
ER -