Root-$n$ Asymptotically Normal Maximum Score Estimation

2026-04-14

AI Summary

This study addresses the well-known limitations of traditional maximum score estimation in binary choice models, which suffers from a convergence rate slower than √n and a nonstandard limiting distribution that impedes conventional statistical inference. The authors propose a novel estimator based on a strictly concave, smooth surrogate score function. Under newly established and verifiable primitive conditions, this approach achieves both √n-consistency and asymptotic normality. By integrating smoothing techniques, strict concavity optimization theory, and asymptotic analysis, the proposed estimator enables standard inferential procedures. Monte Carlo simulations confirm its √n convergence rate, asymptotic normality, and valid inference performance in finite samples.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

The maximum score method (Manski, 1975, 1985) is a powerful approach for binary choice models, yet it is known to face both practical and theoretical challenges. In particular, the estimator converges at a slower-than-root-$n$ rate to a nonstandard limiting distribution. We investigate conditions under which strictly concave surrogate score functions can be employed to achieve identification through a smooth criterion function. This criterion enables root-$n$ convergence to a normal limiting distribution. While the conditions to guarantee these desired properties are nontrivial, we characterize them in terms of primitive conditions. Extensive simulation studies support, the root-$n$ convergence rate, the asymptotic normality, and the validity of the standard inference methods.

Problem

• maximum score estimation
• binary choice models
• root-n convergence
• asymptotic normality
• nonstandard limiting distribution

Innovation

• maximum score estimation
• root-n consistency
• asymptotic normality
• surrogate score functions
• binary choice models