arXiv subjects

Jacob Dorn

Publications and source records attributed to Jacob Dorn.

5 recordsLinked to original sources

arXiv2025

How Much Weak Overlap Can Doubly Robust T-Statistics Handle?

In the presence of sufficiently weak overlap, it is known that no regular root-n-consistent estimators exist and standard estimators may fail to be asymptotically normal. This paper shows that a thresholded version of the standard doubly robust estimator is asymptotically normal with well-calibrated Wald confidence intervals even when constructed using nonparametric estimates of the propensity score and conditional mean outcome. The analysis implies a cost of weak overlap in terms of black-box nuisance rates, borne when the semiparametric bound is infinite, and the contribution of outcome smoothness to the outcome regression rate, which is incurred even when the semiparametric bound is finite. As a byproduct of this analysis, I show that under weak overlap, the optimal global regression rate is the same as the optimal pointwise regression rate, without the usual polylogarithmic penalty. The high-level conditions yield new rules of thumb for thresholding in practice. In simulations, thresholded AIPW can exhibit moderate overrejection in small samples, but I am unable to reject a null hypothesis of exact coverage in large samples. In an empirical application, the clipped AIPW estimator that targets the standard average treatment effect yields similar precision to a heuristic 10% fixed-trimming approach that changes the target sample.

econ.EM↗

arXiv2023

Sensitivity Analysis for Linear Estimators

We propose a novel sensitivity analysis framework for linear estimators with identification failures that can be viewed as seeing the wrong outcome distribution. Our approach measures the degree of identification failure through the change in measure between the observed distribution and a hypothetical target distribution that would identify the causal parameter of interest. The framework yields a sensitivity analysis that generalizes existing bounds for Average Potential Outcome (APO), Regression Discontinuity (RD), and instrumental variables (IV) exclusion failure designs. Our partial identification results extend results from the APO context to allow even unbounded likelihood ratios. Our proposed sensitivity analysis consistently estimates sharp bounds under plausible conditions and estimates valid bounds under mild conditions. We find that our method performs well in simulations even when targeting a discontinuous and nearly infinite bound.

econ.EM↗

arXiv2023

B-Learner: Quasi-Oracle Bounds on Heterogeneous Causal Effects Under Hidden Confounding

Estimating heterogeneous treatment effects from observational data is a crucial task across many fields, helping policy and decision-makers take better actions. There has been recent progress on robust and efficient methods for estimating the conditional average treatment effect (CATE) function, but these methods often do not take into account the risk of hidden confounding, which could arbitrarily and unknowingly bias any causal estimate based on observational data. We propose a meta-learner called the B-Learner, which can efficiently learn sharp bounds on the CATE function under limits on the level of hidden confounding. We derive the B-Learner by adapting recent results for sharp and valid bounds of the average treatment effect (Dorn et al., 2021) into the framework given by Kallus & Oprescu (2023) for robust and model-agnostic learning of conditional distributional treatment effects. The B-Learner can use any function estimator such as random forests and deep neural networks, and we prove its estimates are valid, sharp, efficient, and have a quasi-oracle property with respect to the constituent estimators under more general conditions than existing methods. Semi-synthetic experimental comparisons validate the theoretical findings, and we use real-world data to demonstrate how the method might be used in practice.

cs.LG↗

arXiv2021

Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding

We consider the problem of constructing bounds on the average treatment effect (ATE) when unmeasured confounders exist but have bounded influence. Specifically, we assume that omitted confounders could not change the odds of treatment for any unit by more than a fixed factor. We derive the sharp partial identification bounds implied by this assumption by leveraging distributionally robust optimization, and we propose estimators of these bounds with several novel robustness properties. The first is double sharpness: our estimators consistently estimate the sharp ATE bounds when one of two nuisance parameters is misspecified and achieve semiparametric efficiency when all nuisance parameters are suitably consistent. The second is double validity: even when most nuisance parameters are misspecified, our estimators still provide valid but possibly conservative bounds for the ATE and our Wald confidence intervals remain valid even when our estimators are not asymptotically normal. As a result, our estimators provide a highly credible method for sensitivity analysis of causal inferences.

stat.ME↗

arXiv2021

Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing

Inverse propensity weighting (IPW) is a popular method for estimating treatment effects from observational data. However, its correctness relies on the untestable (and frequently implausible) assumption that all confounders have been measured. This paper introduces a robust sensitivity analysis for IPW that estimates the range of treatment effects compatible with a given amount of unobserved confounding. The estimated range converges to the narrowest possible interval (under the given assumptions) that must contain the true treatment effect. Our proposal is a refinement of the influential sensitivity analysis by Zhao, Small, and Bhattacharya (2019), which we show gives bounds that are too wide even asymptotically. This analysis is based on new partial identification results for Tan (2006)'s marginal sensitivity model.

math.ST↗