Songliang Chen, Fang Han
arXiv 8 Nov 2024 · Mathematics — Statistics Theory
arXiv:2411.05758 · PDF · DOI · OpenAlex · Extracted main text
This paper examines the limiting variance of nearest neighbor matching estimators for average treatment effects with a fixed number of matches. We present, for the first time, a closed-form expression for this limit. Here the key is the establishment of the limiting second moment of the catchment area's volume, which resolves a question of Abadie and Imbens. At the core of our approach is a new universality theorem on the measures of high-order Voronoi cells, extending a result by Devroye, Gy\"orfi, Lugosi, and Walk.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
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 | Abadie, A. and Imbens, G. W (2006) Large sample properties of matching estimators for average treatment effects | 1.000 | 13 | 4 | 100% |
| 2 | Lin, Z., Ding, P., and Han, F (2023) Estimation based on nearest neighbor matching: from density ratio to average treatment effect self | 1.000 | 6 | 3 | 100% |
| 3 | Devroye, L., Györfi, L., Lugosi, G., and Walk, H (2017) On the measure of Voronoi cells | 1.000 | 5 | 4 | 100% |
| 4 | Abadie, A. and Imbens, G. W (2011) Bias-corrected matching estimators for average treatment effects | 0.874 | 6 | 2 | 100% |
| 5 | Abadie, A. and Imbens, G. W (2016) Matching on the estimated propensity score | 0.644 | 2 | 2 | 100% |
| 6 | Voronoi, G (1908) Nouvelles applications des paramètres continus à la théorie des formes quadratiques. deuxième mémoire. recherches sur les parall… | 0.644 | 2 | 2 | 100% |
| 7 | Biau, G. and Devroye, L (2015) Lectures on the Nearest Neighbor Method | 0.405 | 1 | 1 | 100% |
| 8 | Friedman, J. H. and Rafsky, L. C (1979) Multivariate generalizations of the Wald-Wolfowitz and Smirnov two-sample tests | 0.405 | 1 | 1 | 100% |
| 9 | Bickel, P. J. and Breiman, L (1983) Sums of functions of nearest neighbor distances, moment bounds, limit theorems and a goodness of fit test | 0.405 | 1 | 1 | 100% |
| 10 | Abadie, A. and Imbens, G (2002) Simple and bias-corrected matching estimators for average treatment effects | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 32 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Post-Matching Two-Way Fixed Effects Estimation | 0.822 | 9 | 3 |