The Matching Methodology: Some Statistical Properties

Matching is defined as the methodology of merging micro-data to create larger files of data. Matching is often done to extract statistical information which cannot be obtained from the individual files that are incomplete. Current federal statistical practice involving multivariate file- merging techniques is typically not based on a formal statistical theory. In view of this situation, a survey on matching is given. All known models for matching are presented under a unified framework, which consists of three situations involving the same or similar individuals. The properties of a maximum likelihood strategy to match files of data involving the same individuals are derived via ranks and order-statistics from bivariate populations. In addition, the properties of this strategy have been examined with respect to a more reasonable criterion called epsilon-correct matching. Asymptotic results for such situations, including the Poisson approximation for the distribution of the number of correct matches, and convergence in probability of the average number of epsilon-correct matches, have been derived. Small-sample properties, like the monotone behavior of the expected number of matches with respect to the dependence of parameters of the underlying models, have been proved.