Honest Inference for High-Dimensional Linear Models

Dennis Lim, Pengjin Min, Jonathan H. W. Tan and Jiezheng Wei

Papers from arXiv.org

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.

Date: 2026-10
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