Ying Jin
arXiv 7 Oct 2026 · Mathematics — Statistics Theory
arXiv:2610.10873 · PDF · Extracted main text
One-to-one matching without replacement is a classical approach to constructing comparable treated and control samples in the design of observational studies. It pairs each treated unit with a distinct control while minimizing a covariate distance objective. With continuous covariates, the matched pairs generally remain inexact, which contributes to bias in downstream analysis. Its key theoretical properties, such as the resulting imbalance between matched pairs and when it is negligible to support valid inference, remain unclear. In this paper, we analyze one-to-one matching based on $d$-dimensional, continuous covariates with a quadratic covariate-distance objective. First, we find that when $d\leq 3$, under standard conditions on the propensity score ensuring abundant control samples near each treated sample, the imbalance (difference between within-group averages) is root-$n$ negligible uniformly over the family of smooth functions with a common first- and second-order derivative bound. However, such balance is subject to a dimension restriction, as we construct examples in which the imbalance is root-$n$ non-negligible when $d=4$ and dominates root-$n$ rate when $d>4$. Second, we show that when $d\leq 3$, the matched design allows valid Wald-type and bootstrap inference for the average treatment effect on the treated, distributional treatment effects, and quantile treatment effects. Thus, the same outcome-blind matched design supports various downstream inferences without having to tailor the design to the targets. Finally, paired randomization inference based on the matched design is asymptotically valid in the super-population sense for $d\leq 3$ but can fail when $d=4$. We corroborate the theoretical results with numerical experiments.
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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 | Guo, Kevin and Rothenhäusler, Dominik (2023) On the Statistical Role of Inexact Matching in Observational Studies | 1.000 | 9 | 5 | 100% |
| 2 | Abadie, Alberto and Imbens, Guido W (2012) A Martingale Representation for Matching Estimators | 1.000 | 7 | 3 | 100% |
| 3 | Abadie, Alberto and Spiess, Jann (2022) Robust Post-Matching Inference | 1.000 | 5 | 3 | 100% |
| 4 | Sävje, Fredrik (2022) On the Inconsistency of Matching without Replacement | 0.811 | 4 | 2 | 100% |
| 5 | Bind, Marie-Abele C and Rubin, Donald B (2019) Bridging observational studies and randomized experiments by embedding the former in the latter | 0.737 | 3 | 2 | 100% |
| 6 | Rosenbaum, Paul R (1989) Optimal matching for observational studies | 0.737 | 3 | 2 | 100% |
| 7 | Zhang, Bo and Small, Dylan S and Lasater, Karen B and McHugh, Matt a… (2023) Matching one sample according to two criteria in observational studies | 0.737 | 3 | 2 | 100% |
| 8 | Abadie, Alberto and Imbens, Guido W (2006) Large Sample Properties of Matching Estimators for Average Treatment Effects | 0.644 | 2 | 2 | 100% |
| 9 | Lin, Zhexiao and Ding, Peng and Han, Fang (2023) Estimation based on nearest neighbor matching: from density ratio to average treatment effect | 0.511 | 2 | 1 | 100% |
| 10 | Rosenbaum, Paul R and Rubin, Donald B (1985) Constructing a control group using multivariate matched sampling methods that incorporate the propensity score | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 33 scored citations.