A fast algorithm for detecting maximal number of matched pairs under a given caliper

We present a new algorithm which detects the maximal number of matched disjoint pairs satisfying a given caliper when the matching is done with respect to a scalar index (e.g., propensity score), and constructs a corresponding matching. We assume the caliper to be a Lipschitz function of the observations. If the observations are ordered with respect to the index then the matching needs O(N) operations, where N is the total number of objects to be matched. The case of 1-to-n matching is also considered.