arXiv 29 Nov 2025 · Econometrics
arXiv:2512.00265 · PDF · DOI · OpenAlex · Extracted main text
This paper is an exposition of how BRIDGE and adaptive LASSO can be used in a two-stage least squares problem, to estimate the second-stage coefficients when the number of parameters p in both stages is growing with the sample size n. Facing a larger class of problems compared to the usual analysis in the literature, i.e., replacing the assumption of normal with sub-Gaussian errors, I prove that both methods ensure model selection consistency and oracle efficiency even when the number of instruments and covariates exceeds the sample size. For BRIDGE, I also prove that if the former is growing but slower than the latter, the same properties hold even without sub-Gaussian errors. When p is greater than n, BRIDGE requires a slightly weaker set of assumptions to have the desirable properties, as adaptive LASSO requires a good initial estimator of the relevant weights. However, adaptive LASSO is expected to be much faster computationally, so the methods are competitive on different fronts and the one that is recommended depends on the researcher's resources.
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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 | Jian Huang, Joel L Horowitz, and Shuangge Ma (2008) Asymptotic properties of bridge estimators in sparse high-dimensional regression models | 0.894 | 7 | 6 | 71% |
| 2 | Jian Huang, Shuangge Ma, and Cun-Hui Zhang Adaptive lasso for sparse high-dimensional regression models | 0.794 | 6 | 3 | 50% |
| 3 | David Gold, Johannes Lederer, and Jing Tao (2020) Inference for high-dimensional instrumental variables regression | 0.644 | 2 | 2 | 100% |
| 4 | Jian Huang and Shuangge Ma (2010) Variable selection in the accelerated failure time model via the bridge method | 0.511 | 2 | 1 | 100% |
| 5 | Fatemeh Bahador, Ayyub Sheikhi, and Alireza Arabpour (2024) A two-stage bridge estimator for regression models with endogeneity based on control function method | 0.405 | 1 | 1 | 100% |
| 6 | Alexandre Belloni, Daniel Chen, Victor Chernozhukov, and Christian H… (2012) Sparse models and methods for optimal instruments with an application to eminent domain | 0.405 | 1 | 1 | 100% |
| 7 | Mehmet Caner and Hao Helen Zhang (2014) Adaptive elastic net for generalized methods of moments | 0.405 | 1 | 1 | 100% |
| 8 | Mehmet Caner and Qingliang Fan (2015) Hybrid generalized empirical likelihood estimators: Instrument selection with adaptive lasso | 0.405 | 1 | 1 | 100% |
| 9 | Jianqing Fan and Runze Li (2001) Variable selection via nonconcave penalized likelihood and its oracle properties | 0.405 | 1 | 1 | 100% |
| 10 | Jianqing Fan and Yuan Liao (2014) Endogeneity in high dimensions | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 26 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Post-selection inference for network structure 1 | 0.405 | 1 | 1 |