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Recently, there has been significant interest in linear regression in thesituation where predictors and responses are not observed in matching pairscorresponding to the same statistical unit as a consequence of separate datacollection and uncertainty in data integration. Mismatched pairs canconsiderably impact the model fit and disrupt the estimation of regressionparameters. In this paper, we present a method to adjust for such mismatchesunder ``partial shuffling" in which a sufficiently large fraction of(predictors, response)-pairs are observed in their correct correspondence. Theproposed approach is based on a pseudo-likelihood in which each term takes theform of a two-component mixture density. Expectation-Maximization schemes areproposed for optimization, which (i) scale favorably in the number of samples,and (ii) achieve excellent statistical performance relative to an oracle thathas access to the correct pairings as certified by simulations and casestudies. In particular, the proposed approach can tolerate considerably largerfraction of mismatches than existing approaches, and enables estimation of thenoise level as well as the fraction of mismatches. Inference for the resultingestimator (standard errors, confidence intervals) can be based on establishedtheory for composite likelihood estimation. Along the way, we also propose astatistical test for the presence of mismatches and establish its consistencyunder suitable conditions.

A Pseudo-Likelihood Approach to Linear Regression with Partially Shuffled Data