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Identification of matching records in multiple files can be a challenging anderror-prone task. Linkage error can considerably affect subsequent statisticalanalysis based on the resulting linked file. Several recent papers have studiedpost-linkage linear regression analysis with the response variable in one fileand the covariates in a second file from the perspective of the "Broken SampleProblem" and "Permuted Data". In this paper, we present an extension of thisline of research to exponential family response given the assumption of a smallto moderate number of mismatches. A method based on observation-specificoffsets to account for potential mismatches and $\ell_1$-penalization isproposed, and its statistical properties are discussed. We also presentsufficient conditions for the recovery of the correct correspondence betweencovariates and responses if the regression parameter is known. The proposedapproach is compared to established baselines, namely the methods byLahiri-Larsen and Chambers, both theoretically and empirically based onsynthetic and real data. The results indicate that substantial improvementsover those methods can be achieved even if only limited information about thelinkage process is available.

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