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Estimation based on nearest neighbor matching: from density ratio to average treatment effect

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  • Zhexiao Lin
  • Peng Ding
  • Fang Han

Abstract

Nearest neighbor (NN) matching as a tool to align data sampled from different groups is both conceptually natural and practically well-used. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN matching under, however, a crucial assumption that the number of NNs, $M$, is fixed. This manuscript reveals something new out of their study and shows that, once allowing $M$ to diverge with the sample size, an intrinsic statistic in their analysis actually constitutes a consistent estimator of the density ratio. Furthermore, through selecting a suitable $M$, this statistic can attain the minimax lower bound of estimation over a Lipschitz density function class. Consequently, with a diverging $M$, the NN matching provably yields a doubly robust estimator of the average treatment effect and is semiparametrically efficient if the density functions are sufficiently smooth and the outcome model is appropriately specified. It can thus be viewed as a precursor of double machine learning estimators.

Suggested Citation

  • Zhexiao Lin & Peng Ding & Fang Han, 2021. "Estimation based on nearest neighbor matching: from density ratio to average treatment effect," Papers 2112.13506, arXiv.org.
    • Handle: RePEc:arx:papers:2112.13506
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    References listed on IDEAS

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    Cited by:

    1. Zhexiao Lin & Fang Han, 2022. "On regression-adjusted imputation estimators of the average treatment effect," Papers 2212.05424, arXiv.org, revised Jan 2023.
    2. David Arbour & Harsh Parikh & Bijan Niknam & Elizabeth Stuart & Kara Rudolph & Avi Feller, 2025. "Regularizing Extrapolation in Causal Inference," Papers 2509.17180, arXiv.org, revised Oct 2025.

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