ReLU-Based and DNN-Based Generalized Maximum Score Estimators

Xiaohong Chen, Wayne Yuan Gao and Likang Wen
Additional contact information
Xiaohong Chen: Department of Economics and Cowles Foundation for Research in Economics, Yale University
Wayne Yuan Gao: Department of Economics, University of Pennsylvania
Likang Wen: Department of Applied Mathematics and Statistics, Johns Hopkins University

No 2476, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We propose a new formulation of the maximum score estimator that uses compositions of rectified linear unit (ReLU) functions, instead of indicator functions as in Manski (1975, 1985), to encode the sign alignment restrictions. Since the ReLU function is Lipschitz, our new ReLU-based maximum score criterion function is substantially easier to optimize using standard gradient-based optimization pacakges. We also show that our ReLU-based maximum score (RMS) estimator can be generalized to an umbrella framework defined by multi-index single-crossing (MISC) conditions, while the original maximum score estimator cannot be applied. We establish the n^(-s/(2s+1)) convergence rate and asymptotic normality for the RMS estimator under order-s Holder smoothness. In addition, we propose an alternative estimator using a further reformulation of RMS as a special layer in a deep neural network (DNN) architecture, which allows the estimation procedure to be implemented via state-of-the-art software and hardware for DNN.

Pages: 71 pages
Date: 2025-11-25
References: Add references at CitEc
Citations:

Downloads: (external link)
https://cowles.yale.edu/sites/default/files/2025-12/d2476.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cwl:cwldpp:2476

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Brittany Ladd ().