Uncertainty Quantification in Linear Regression With Mismatched Data

TMLR Paper4989 Authors

Abstract: The fundamental assumption in regression analysis that each response-predictor pair corresponds to the same observational unit is not always valid, especially with mismatched data. This paper presents a novel approach for uncertainty quantification in linear regression when data mismatch occurs. Using the generalized fiducial inference framework, we develop a method to generate fiducial samples for constructing confidence intervals and measuring uncertainty in key regression parameters. We establish the theoretical properties of our approach and demonstrate its practical effectiveness through empirical tests on both simulated and real datasets. To our knowledge, this is the first study to explore uncertainty quantification for mismatched data in linear regression.

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Antti_Honkela1

Submission Number: 4989