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

TL;DR

This paper demonstrates that the maximum score estimator becomes asymptotically normal under multiway dependence, enabling easier statistical inference through a new M-estimation theory and bootstrap validation.

Contribution

It introduces a novel M-estimation framework for non-smooth functions under multiway dependence, showing asymptotic normality and proposing a bootstrap inference method.

Findings

Maximum score estimator attains asymptotic normality under multiway dependence.

Develops a general M-estimation theory for non-smooth objectives with dependence.

Validates a bootstrap procedure for inference in this setting.

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.