Nan Liu, Yanbo Liu, Yuya Sasaki, Yuanyuan Wan
arXiv 15 Apr 2026 · Econometrics
arXiv:2604.13399 · PDF · DOI · OpenAlex · Extracted main text
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Klein, R. W. and R. H. Spady (1993) An efficient semiparametric estimator for binary response models | 0.737 | 3 | 2 | 100% |
| 2 | Manski, C. F (1975) Maximum score estimation of the stochastic utility model of choice | 0.644 | 2 | 2 | 100% |
| 3 | Manski, C. F (1985) Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator | 0.644 | 2 | 2 | 100% |
| 4 | Bartlett, P. L., M. I. Jordan, and J. D. McAuliffe (2006) Convexity, classification, and risk bounds | 0.511 | 2 | 1 | 100% |
| 5 | Horowitz, J. L (1992) A smoothed maximum score estimator for the binary response model | 0.511 | 2 | 1 | 100% |
| 6 | Liu, N., Y. Liu, Y. Sasaki, and Y. Wan (2025) Nonparametric uniform inference in binary classification and policy values self | 0.511 | 2 | 1 | 100% |
| 7 | Abrevaya, J. and J. Huang (2005, July) (2005) On the bootstrap of the maximum score estimator | 0.405 | 1 | 1 | 100% |
| 8 | Babii, A., E. Ghysels, and X. Chen (2020) Binary choice with asymmetric loss in a data-rich environment: Theory and an application to racial justice | 0.405 | 1 | 1 | 100% |
| 9 | Bickel, P. J., F. Götze, and W. R. van Zwet (2011) Resampling fewer than n observations: gains, losses, and remedies for losses | 0.405 | 1 | 1 | 100% |
| 10 | Cattaneo, M. D., M. Jansson, and K. Nagasawa (2020) Bootstrap-based inference for cube root asymptotics | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 29 scored citations.