Zhexiao Lin, Peng Ding, Fang Han
arXiv 27 Dec 2021 · Mathematics — Statistics Theory · publishedEconometrica (2023) · 4 citations (OpenAlex)
arXiv:2112.13506 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Noshad, M., Moon, K. R., Sekeh, S. Y., and Hero, A. O (2017) Direct estimation of information divergence using nearest neighbor ratios | 1.000 | 8 | 3 | 100% |
| 2 | Abadie, A. and Imbens, G. W (2006) Large sample properties of matching estimators for average treatment effects | 0.987 | 26 | 5 | 96% |
| 3 | Abadie, A. and Imbens, G. W (2011) Bias-corrected matching estimators for average treatment effects | 0.983 | 20 | 4 | 95% |
| 4 | Abadie, A. and Imbens, G. W (2012) A martingale representation for matching estimators | 0.928 | 4 | 3 | 100% |
| 5 | Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C… (2018) Double/debiased machine learning for treatment and structural parameters | 0.863 | 14 | 3 | 64% |
| 6 | Kremer, J., Gieseke, F., Pedersen, K. S., and Igel, C (2015) Nearest neighbor density ratio estimation for large-scale applications in astronomy | 0.843 | 3 | 3 | 100% |
| 7 | Lima, M., Cunha, C. E., Oyaizu, H., Frieman, J., Lin, H., and Sheldo… (2008) Estimating the redshift distribution of photometric galaxy samples | 0.843 | 3 | 3 | 100% |
| 8 | Zhao, P. and Lai, L (2020) Minimax optimal estimation of KL divergence for continuous distributions | 0.843 | 3 | 3 | 100% |
| 9 | Bang, H. and Robins, J. M (2005) Doubly robust estimation in missing data and causal inference models | 0.811 | 4 | 2 | 100% |
| 10 | Hahn, J (1998) On the role of the propensity score in efficient semiparametric estimation of average treatment effects | 0.811 | 4 | 2 | 100% |
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