### Abstract

We present a new algorithm which detects the maximal possible number of matched disjoint pairs satisfying a given caliper when a bipartite matching is done with respect to a scalar index (e.g., propensity score), and constructs a corresponding matching. Variable width calipers are compatible with the technique, provided that the width of the caliper is a Lipschitz function of the index. If the observations are ordered with respect to the index then the matching needs O(N) operations, where N is the total number of subjects to be matched. The case of 1-to-n matching is also considered. We offer also a new fast algorithm for optimal complete one-to-one matching on a scalar index when the treatment and control groups are of the same size. This allows us to improve greedy nearest neighbor matching on a scalar index.

Original language | English |
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Pages (from-to) | 477-495 |

Number of pages | 19 |

Journal | Methodology and Computing in Applied Probability |

Volume | 22 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jun 2020 |

### Keywords

- Matching with caliper
- Nearest neighbor matching
- Propensity score matching
- Variable width caliper