# Data Fusion for Errors-in-Variables

arXiv: https://arxiv.org/abs/2610.07048 · HTML: https://mlsanity.com/paper/2610.07048/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 41 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 3 of 3)

- [Transfer Learning with General Estimating Equations](https://mlsanity.com/paper/2410.04398/) (2024)
- [Total robustness in Bayesian Nonlinear Regression](https://mlsanity.com/paper/2510.03131/) (2025)
- [Simulation-free extrapolation for misspecified models induced by categorizing an error-prone continuous covariate](https://mlsanity.com/paper/2509.06118/) (2025)

## Abstract (arXiv)

We study errors-in-variables problems in which a target study contains only a single error-prone surrogate of an unobserved exposure, while an external source study provides repeated surrogate measurements from a different population. The measurement error distribution is allowed to depend on the observed error-free variables, and the error-free variable distribution itself may differ between studies. We introduce a conditional transportability assumption that enables the use of external repeated measurements under source-target heterogeneity. Together with additional replicate-error conditions, it identifies the target conditional measurement-error distribution. Building on this identification result, we develop a data-fusion estimator for a broad class of target functionals. The estimator combines conditional deconvolution, flexible nuisance estimation, and orthogonal correction that reduces first-order sensitivity to nuisance estimation. For the proposed estimator, we develop a unified spectral theory covering both diffuse-spectrum and finite atomic-spectrum target functionals, derive a general asymptotic expansion, and establish consistency and target-specific convergence-rate bounds. The resulting convergence-rate bounds depend jointly on the spectral properties of the measurement error, the latent exposure, and the target functional. For finite atomic-spectrum targets, we further establish joint Gaussian and bootstrap limits, yielding inference for smooth moment transformations under an additional centering condition. In the reported simulations, Fuse-EIV has small bias for the primary exposure-related coefficient. Applications to the National Health and Nutrition Examination Survey illustrate how accounting for population heterogeneity and error heteroscedasticity can change empirical conclusions.