Denis Chetverikov, Jesper Riis-Vestergaard Sørensen
arXiv 10 Apr 2021 · Mathematics — Statistics Theory · publishedJournal of Political Economy (2025) · 3 citations (OpenAlex)
arXiv:2104.04716 · PDF · DOI · OpenAlex · Extracted main text
We develop a new method for selecting the penalty parameter for $\ell_{1}$-penalized M-estimators in high dimensions, which we refer to as bootstrapping after cross-validation. We derive rates of convergence for the corresponding $\ell_1$-penalized M-estimator and also for the post-$\ell_1$-penalized M-estimator, which refits the non-zero entries of the former estimator without penalty in the criterion function. We demonstrate via simulations that our methods are not dominated by cross-validation in terms of estimation errors and can outperform cross-validation in terms of inference. As an empirical illustration, we revisit Fryer Jr (2019), who investigated racial differences in police use of force, and confirm his findings.
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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 | Fryer Jr, R. G (2019) An empirical analysis of racial differences in police use of force | 1.000 | 12 | 3 | 100% |
| 2 | Negahban, S. N., P. Ravikumar, M. J. Wainwright, and B. Yu (2012) A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers | 0.956 | 8 | 4 | 88% |
| 3 | van de Geer, S. A (2008) High-Dimensional Generalized Linear Models and the Lasso | 0.894 | 7 | 3 | 71% |
| 4 | Wainwright, M. J (2019) High-dimensional statistics: A non-asymptotic viewpoint | 0.843 | 3 | 3 | 100% |
| 5 | Belloni, A. and V. Chernozhukov (2011) a): $_1$-penalized quantile regression in high-dimensional sparse models | 0.811 | 4 | 2 | 100% |
| 6 | Belloni, A., V. Chernozhukov, and Y. Wei (2016) Post-selection inference for generalized linear models with many controls | 0.737 | 10 | 3 | 40% |
| 7 | Honoré, B. E (1992) Trimmed LAD and least squares estimation of truncated and censored regression models with fixed effects | 0.737 | 3 | 2 | 100% |
| 8 | Belloni, A., V. Chernozhukov, D. Chetverikov, C. Hansen, and K. Kato (2018) a): High-dimensional econometrics and regularized GMM | 0.693 | 12 | 3 | 33% |
| 9 | Bickel, P. J., Y. Ritov, and A. B. Tsybakov (2009) Simultaneous analysis of Lasso and Dantzig selector | 0.644 | 4 | 2 | 50% |
| 10 | Chernozhukov, V., D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W… (2018) Double/debiased machine learning for treatment and structural parameters | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 61 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Triple/Double-Debiased Lasso | 0.644 | 2 | 2 |
| 2 | High Dimensional Binary Choice Model with Unknown Heteroskedasticity or Instrumental Variables | 0.405 | 1 | 1 |
| 3 | 0.5cmLow-Rank Estimation of Nonlinear Panel Data Models | 0.405 | 1 | 1 |