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

arXiv: https://arxiv.org/abs/2604.24660 · HTML: https://mlsanity.com/paper/2604.24660/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Applied Causal Inference Powered by ML and AI](https://mlsanity.com/paper/2403.02467/) (2024)
- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)
- [Source Condition Double Robust Inference on Functionals of Inverse Problems](https://mlsanity.com/paper/2307.13793/) (2023)
- [Nonparametric Instrumental Variable Inference with Many Weak Instruments](https://mlsanity.com/paper/2505.07729/) (2025)
- [Nonparametric Instrumental Variable Regression with Observed Covariates](https://mlsanity.com/paper/2511.19404/) (2025)
- [The purpose of an estimator is what it does: Misspecification, estimands, and over-identification](https://mlsanity.com/paper/2508.13076/) (2025)

## Abstract (arXiv)

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.