Data Fusion for Errors-in-Variables
Abstract
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.
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BibTeX
@misc{zhao2026data,
title = {{Data Fusion for Errors-in-Variables}},
author = {Huali Zhao and Molei Liu and Tianying Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07048},
eprint = {2610.07048},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07048},
}
RIS
TY - UNPB
TI - Data Fusion for Errors-in-Variables
AU - Huali Zhao
AU - Molei Liu
AU - Tianying Wang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07048
UR - https://arxiv.org/abs/2610.07048
AB - 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.
ER -