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Nonparametric Instrumental Variable Analysis Without Structural Equations: Debiased Inference on Functionals of Inverse Problems with No Solutions

Author

Listed:
  • Zikai Shen
  • Nathan Kallus
  • Dimitri Meunier
  • Houssam Zenati
  • Arthur Gretton
  • Aur'elien Bibaut

Abstract

We consider debiased inference on finite-dimensional functionals of infinite-dimensional least-squares solutions to inverse problems as a way to avoid having to assume exact solutions exist. Such assumptions are substantive and not innocuous, and their failure may imperil inference when we impose them on the statistical model. Our approach instead allows us to conduct inference on a quantity that is defined regardless of solutions existing and coincides with the usual estimands when they do. For the case of instrumental variables, this means we can motivate the analysis with structural models but these do not need to hold exactly for the semiparametric inferential procedure to remain valid.

Suggested Citation

  • Zikai Shen & Nathan Kallus & Dimitri Meunier & Houssam Zenati & Arthur Gretton & Aur'elien Bibaut, 2026. "Nonparametric Instrumental Variable Analysis Without Structural Equations: Debiased Inference on Functionals of Inverse Problems with No Solutions," Papers 2604.24660, arXiv.org, revised May 2026.
    • Handle: RePEc:arx:papers:2604.24660
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    References listed on IDEAS

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