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Bias-Aware Inference in Regularized Regression Models

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arxiv 2012.14823 v2 pith:4I4HEEQZ submitted 2020-12-29 econ.EM stat.ME

Timothy B. Armstrong , Michal Kolesár , Soonwoo Kwon This is my paper
classification econ.EMstat.ME
keywords estimatorsregressionunderbiasbias-awarederiveinferencenumber
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Robust Inference for Weighted Estimands

    econ.EM 2026-07 accept novelty 7.0 of 10

    The paper constructs minimax-bias estimators and uniformly valid confidence intervals for weighted estimands by bounding differences via parameter heterogeneity and weight distance.

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    Develops higher-order influence function estimators for implicitly defined parameters in non-separable structural models using U-processes theory.

  3. Local Asymptotic Power of Honest Confidence Intervals

    econ.EM 2026-07 accept novelty 6.5 of 10

    Honest bias-aware confidence intervals have zero local asymptotic power when the bias bound dominates the sampling rate, a loss intrinsic to honesty itself rather than any particular construction.

  4. Identification and Robust Inference for Multiple Treatment Effects with Possibly Invalid Instruments

    stat.ME 2026-07 conditional novelty 6.0 of 10

    A sampling-based confidence interval maintains nominal coverage and n^{-1/2} length for multiple treatment effects in linear IV models with possibly invalid instruments, under generalized majority/plurality conditions.

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