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Uniform inference for kernel instrumental variable regres...
[Submitted on 26 Nov 2025 (v1), last revised 5 Jul 2026 (this ve · 2025-11-27 · via stat updates on arXiv.org

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Abstract:Instrumental variable regression is a foundational tool for causal analysis across the social and biomedical sciences. Recent advances use kernel methods to estimate nonparametric causal relationships, with general data types, while retaining a simple closed-form expression. Empirical researchers ultimately need reliable inference on causal estimates; however, uniform confidence sets for the method remain unavailable. To fill this gap, we develop valid and sharp confidence sets for kernel instrumental variable regression, allowing general nonlinearities and data types. Computationally, our bootstrap procedure requires only a single run of the kernel instrumental variable regression estimator. Theoretically, it relies on the same key assumptions. Overall, we provide a practical procedure for inference that substantially increases the value of kernel methods for causal analysis.

Submission history

From: Marvin Lob [view email]
[v1] Wed, 26 Nov 2025 17:18:21 UTC (71 KB)
[v2] Tue, 20 Jan 2026 13:56:28 UTC (73 KB)
[v3] Sun, 5 Jul 2026 14:46:38 UTC (75 KB)