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

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