Online inference under over-parameterized models with hidden confounders
Authors
Paper Information
-
Journal:
Journal of the Royal Statistical Society Series B -
DOI:
10.1093/jrsssb/qkag110 -
Published:
June 29, 2026 -
Added to Tracker:
Jun 30, 2026
Abstract
Abstract In this paper, we study online estimation and inference of regression coefficients in the presence of hidden confounders by leveraging over-parameterized models. Unlike existing offline approaches that rely on factor and sparse models, our closed-form estimator simultaneously removes hidden-confounder bias and is directly applicable to streaming data. Using tools from random matrix theory, we analyse phase transition phenomena in the variance of the coefficient estimator that arise as the sample size transitions from being smaller than to larger than the number of predictors. Notably, we show that adding more covariates only slightly affects the estimator’s variance, mitigating concerns about variance inflation in over-parameterized settings. We validate the effectiveness of our method for both individual coefficient inference and multiple testing through simulations and applications to two real datasets.
Author Details
Tao Li
AuthorMengyun Wu
AuthorShuyan Chen
AuthorXingdong Feng
AuthorYeheng Ge
AuthorCitation Information
APA Format
Tao Li
,
Mengyun Wu
,
Shuyan Chen
,
Xingdong Feng
&
Yeheng Ge
(2026)
.
Online inference under over-parameterized models with hidden confounders.
Journal of the Royal Statistical Society Series B
, 10.1093/jrsssb/qkag110.
BibTeX Format
@article{paper1356,
title = { Online inference under over-parameterized models with hidden confounders },
author = {
Tao Li
and Mengyun Wu
and Shuyan Chen
and Xingdong Feng
and Yeheng Ge
},
journal = { Journal of the Royal Statistical Society Series B },
year = { 2026 },
doi = { 10.1093/jrsssb/qkag110 },
url = { https://doi.org/10.1093/jrsssb/qkag110 }
}