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Bias-Aware Inference in Regularized Regression Models

Timothy B. Armstrong, Michal Kolesár, Soonwoo Kwon

arXiv 29 Dec 2020 · Econometrics · 5 citations (OpenAlex)

arXiv:2012.14823 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Zhang, C.-H. and Zhang, S. S (2014) Confidence intervals for low dimensional parameters in high dimensional linear models1.000103100%
2Belloni, A., Chernozhukov, V., and Hansen, C (2014) Inference on treatment effects after selection among high-dimensional controls1.00095100%
3Li, C. M. and Müller, U. K (2021) Linear regression with many controls of limited explanatory power1.00093100%
4Javanmard, A. and Montanari, A (2014) Confidence intervals and hypothesis testing for high-dimensional regression1.00084100%
5van de Geer, S. A., Bühlmann, P., Ritov, Y., and Dezeure, R (2014) On asymptotically optimal confidence regions and tests for high-dimensional models1.00053100%
6Donoho, D. L (1994) Statistical estimation and optimal recovery0.79410350%
7Cai, T. T. and Guo, Z (2017) Confidence intervals for high-dimensional linear regression: Minimax rates and adaptivity0.7946350%
8Low, M. G (1995) Bias-variance tradeoffs in functional estimation problems0.7946350%
9Bühlmann, P. and van de Geer, S. A (2011) Statistics for High-Dimensional Data: Methods, Theory and Applications0.7374350%
10Javanmard, A. and Montanari, A (2018) Debiasing the lasso: Optimal sample size for Gaussian designs0.7374350%

Showing the top 10 of 47 scored citations.

Cited by, within the corpus

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1Estimating Treatment Effects Under Bounded Heterogeneity0.75473
2Robust Estimation and Inference in Panels with Interactive Fixed Effects0.73743
3Short and Simple Confidence Intervals when the Directions of Some Effects are Known0.58531
4Omitted variable bias of Lasso-based inference methods: A finite sample analysis0.40511
5The Fragility of Sparsity0.40511
6Distributionally Robust Synthetic Control: Ensuring Robustness Against Highly Correlated Controls and Weight Shifts0.40511
7Introducing the b-value: combining unbiased and biased estimators from a sensitivity analysis perspective0.40511
8Triple/Double-Debiased Lasso0.40511
9Higher-Order Debiased Estimators for General Treatment Models0.40511
10Local Asymptotic Power of Honest Confidence Intervals0.40511