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Gaussian approximation for maximum score and non-smooth M-estimators with multiway dependence

Harold D. Chiang, Ahnaf Rafi

arXiv 11 Apr 2026 · Econometrics

arXiv:2604.10232 · PDF · DOI · OpenAlex · Extracted main text

Abstract

The maximum score estimator of Manski (1975) provides an elegant approach to estimate slope coefficient in binary choice models without requiring parametric assumptions on the error distribution. However, under i.i.d. sampling, it admits a non-Gaussian limiting distribution and exhibits cube-root asymptotics, which complicates statistical inference. We show that, under multiway dependence, the maximum score estimator attains asymptotic normality at a parametric rate. We obtain this surprising result through the development of a general M-estimation theory that accommodates non-smooth objective functions under multiway dependence. We further propose and establish the validity of a bootstrap procedure for inference.

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35
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Davezies, Laurent and D'Haultfœuille, Xavier and Guyonvarch, Yannick (2021) Empirical Process Results for Exchangeable Arrays0.8434475%
2Arcones, Miguel A and Chen, Zhiqiang and Giné, Evarist (1994) Estimators related to $U$-processes with applications to multivariate medians: asymptotic normality0.81142100%
3Manski, Charles F (1975) Maximum score estimation of the stochastic utility model of choice0.81142100%
4Kim, Jeankyung and Pollard, David (1990) Cube root asymptotics0.7547443%
5Chiang, Harold D and Kato, Kengo and Sasaki, Yuya (2023) Inference for high-dimensional exchangeable arrays self0.73732100%
6Chen, Kaicheng and Chiang, Harold D (2026) Cross-fitting-free debiased machine learning with multiway dependence self0.6597629%
7Manski, Charles F (1985) Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator0.64441100%
8Arcones, Miguel A and Giné, Evarist (1993) Limit theorems for $U$-processes0.64422100%
9Davezies, Laurent and D'Haultfœuille, Xavier and Guyonvarch, Yannick (2025) Analytic inference with two-way clustering0.64422100%
10Menzel, Konrad (2021) Bootstrap with cluster-dependence in two or more dimensions0.64422100%

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