Dennis Lim, Pengjin Min, Jonathan H. W. Tan, Jiezheng Wei
arXiv 12 Oct 2026 · Statistics — Methodology
arXiv:2610.16503 · PDF · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Stanislav Anatolyev and Mikkel Solvsten (2023) Testing many restrictions under heteroskedasticity | 0.874 | 5 | 2 | 100% |
| 2 | Sara van de Geer and Peter Buhlmann and Ya'acov Ritov and Ruben Deze… (2014) ON ASYMPTOTICALLY OPTIMAL CONFIDENCE REGIONS AND TESTS FOR HIGH-DIMENSIONAL MODELS | 0.866 | 20 | 8 | 65% |
| 3 | Caner, Mehmet and Kock, Anders Bredahl (2018) Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative Lasso | 0.807 | 19 | 7 | 53% |
| 4 | Javanmard, Adel and Montanari, Andrea (2014) Confidence intervals and hypothesis testing for high-dimensional regression | 0.737 | 3 | 2 | 100% |
| 5 | Zhang, Cun-Hui and Zhang, Stephanie S (2014) Confidence intervals for low dimensional parameters in high dimensional linear models | 0.737 | 3 | 2 | 100% |
| 6 | Kline, Patrick and Saggio, Raffaele and Sølvsten, Mikkel (2020) Leave-out estimation of variance components | 0.644 | 2 | 2 | 100% |
| 7 | Kuchibhotla, Arun Kumar and Chakrabortty, Abhishek (2022) Moving beyond sub-Gaussianity in high-dimensional statistics: Applications in covariance estimation and linear regression | 0.585 | 10 | 6 | 20% |
| 8 | Dov\`i, Max-Sebastian and Kock, Anders Bredahl and Mavroeidis, Sopho… (2024) A ridge-regularized jackknifed Anderson-Rubin test | 0.585 | 4 | 3 | 25% |
| 9 | Sun, Tingni and Zhang, Cun-Hui (2012) Scaled sparse linear regression | 0.511 | 2 | 2 | 50% |
| 10 | Zou, Hui (2006) The adaptive lasso and its oracle properties | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 38 scored citations.