Timothy B. Armstrong, Michal Kolesár, Soonwoo Kwon
arXiv 29 Dec 2020 · Econometrics · 5 citations (OpenAlex)
arXiv:2012.14823 · PDF · DOI · OpenAlex · Extracted main text
We consider inference on a scalar regression coefficient under a constraint on the magnitude of the control coefficients. A class of estimators based on a regularized propensity score regression is shown to exactly solve a tradeoff between worst-case bias and variance. We derive confidence intervals (CIs) based on these estimators that are bias-aware: they account for the possible bias of the estimator. Under homoskedastic Gaussian errors, these estimators and CIs are near-optimal in finite samples for MSE and CI length. We also provide conditions for asymptotic validity of the CI with unknown and possibly heteroskedastic error distribution, and derive novel optimal rates of convergence under high-dimensional asymptotics that allow the number of regressors to increase more quickly than the number of observations. Extensive simulations and an empirical application illustrate the performance of our methods.
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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 | Zhang, C.-H. and Zhang, S. S (2014) Confidence intervals for low dimensional parameters in high dimensional linear models | 1.000 | 10 | 3 | 100% |
| 2 | Belloni, A., Chernozhukov, V., and Hansen, C (2014) Inference on treatment effects after selection among high-dimensional controls | 1.000 | 9 | 5 | 100% |
| 3 | Li, C. M. and Müller, U. K (2021) Linear regression with many controls of limited explanatory power | 1.000 | 9 | 3 | 100% |
| 4 | Javanmard, A. and Montanari, A (2014) Confidence intervals and hypothesis testing for high-dimensional regression | 1.000 | 8 | 4 | 100% |
| 5 | van de Geer, S. A., Bühlmann, P., Ritov, Y., and Dezeure, R (2014) On asymptotically optimal confidence regions and tests for high-dimensional models | 1.000 | 5 | 3 | 100% |
| 6 | Donoho, D. L (1994) Statistical estimation and optimal recovery | 0.794 | 10 | 3 | 50% |
| 7 | Cai, T. T. and Guo, Z (2017) Confidence intervals for high-dimensional linear regression: Minimax rates and adaptivity | 0.794 | 6 | 3 | 50% |
| 8 | Low, M. G (1995) Bias-variance tradeoffs in functional estimation problems | 0.794 | 6 | 3 | 50% |
| 9 | Bühlmann, P. and van de Geer, S. A (2011) Statistics for High-Dimensional Data: Methods, Theory and Applications | 0.737 | 4 | 3 | 50% |
| 10 | Javanmard, A. and Montanari, A (2018) Debiasing the lasso: Optimal sample size for Gaussian designs | 0.737 | 4 | 3 | 50% |
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