Statistics and Its Interface

Volume 16 (2023)

Number 3

Estimation in exponential family regression based on linked data contaminated by mismatch error

Pages: 379 – 396



Zhenbang Wang (Department of Statistics, George Mason University, Fairfax, Virginia, U.S.A.)

Emanuel Ben-David (U.S. Census, CSRM, Suitland, Maryland, U.S.A.)

Martin Slawski (Department of Statistics, George Mason University, Fairfax, Virginia, U.S.A.)


Identification of matching records in multiple files can be a challenging and error-prone task. Linkage error can considerably affect subsequent statistical analysis based on the resulting linked file. Several recent papers have studied post-linkage linear regression analysis with the response variable in one file and the covariates in a second file from the perspective of the “Broken Sample Problem” and “Permuted Data”. In this paper, we present an extension of this line of research to exponential family response given the assumption of a small to moderate number of mismatches. A method based on observation-specific offsets to account for potential mismatches and $\ell_1$-penalization is proposed, and its statistical properties are discussed. We also present sufficient conditions for the recovery of the correct correspondence between covariates and responses if the regression parameter is known. The proposed approach is compared to established baselines, namely the methods by Lahiri–Larsen and Chambers, both theoretically and empirically based on synthetic and real data. The results indicate that substantial improvements over those methods can be achieved even if only limited information about the linkage process is available.


record linkage, broken sample problem, generalized linear models, penalized estimation, permutation

2010 Mathematics Subject Classification

Primary 62F35, 62J07, 62J12. Secondary 62D99.

Zhenbang Wang and Martin Slawski were partially supported by the NSF Grant CCF-1849876 and NSF-SES 2120-318.

Received 19 February 2021

Accepted 27 January 2022

Published 14 April 2023