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Root-$n$ Asymptotically Normal Maximum Score Estimation

Nan Liu, Yanbo Liu, Yuya Sasaki, Yuanyuan Wan

arXiv 15 Apr 2026 · Econometrics

arXiv:2604.13399 · PDF · DOI · OpenAlex · Extracted main text

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.

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29
references
40
in-text mentions
29
distinct cited
1
self-citations
9,114
main-text words

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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
1Klein, R. W. and R. H. Spady (1993) An efficient semiparametric estimator for binary response models0.73732100%
2Manski, C. F (1975) Maximum score estimation of the stochastic utility model of choice0.64422100%
3Manski, C. F (1985) Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator0.64422100%
4Bartlett, P. L., M. I. Jordan, and J. D. McAuliffe (2006) Convexity, classification, and risk bounds0.51121100%
5Horowitz, J. L (1992) A smoothed maximum score estimator for the binary response model0.51121100%
6Liu, N., Y. Liu, Y. Sasaki, and Y. Wan (2025) Nonparametric uniform inference in binary classification and policy values self0.51121100%
7Abrevaya, J. and J. Huang (2005, July) (2005) On the bootstrap of the maximum score estimator0.40511100%
8Babii, A., E. Ghysels, and X. Chen (2020) Binary choice with asymmetric loss in a data-rich environment: Theory and an application to racial justice0.40511100%
9Bickel, P. J., F. Götze, and W. R. van Zwet (2011) Resampling fewer than n observations: gains, losses, and remedies for losses0.40511100%
10Cattaneo, M. D., M. Jansson, and K. Nagasawa (2020) Bootstrap-based inference for cube root asymptotics0.40511100%

Showing the top 10 of 29 scored citations.