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

Harold D. Chiang and Ahnaf Rafi

Papers from arXiv.org

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.

Date: 2026-04
New Economics Papers: this item is included in nep-dcm and nep-ecm
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