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arXiv · 2504.02694

Semiparametric Inference for Counterfactual Regression under Intervention-Driven Shift

Kwangho Kim
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Abstract

We study counterfactual regression, which maps features to outcomes under hypothetical scenarios that differ from those observed in the data. This problem is central to decision-making under distribution shift, where treatment patterns may change at deployment. We develop a semiparametric framework for counterfactual regression along a prespecified incremental-intervention path. The target is a finite-dimensional constrained projection of counterfactual risk, estimated using cross-fitted influence-function representations of the program components. For smooth programs with fixed constraints and finite-dimensional programs with estimated linear constraints, we establish consistency and local stability of the optimizer under class-specific conditions, and derive pointwise and uniform first-order expansions. These results yield asymptotically valid inference, including simultaneous confidence bands for the counterfactual regression path. Simulations and an application to SMS reminders illustrate the finite-sample performance and practical applicability of the proposed approach.

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Kwangho Kim. 2026-09-03. Semiparametric Inference for Counterfactual Regression under Intervention-Driven Shift. https://arxiv.org/abs/2504.02694

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