A smoothed maximum rank correlation estimator for deep ordinal choice models

Abstract

A smoothed maximum rank correlation (MRC) estimator for ordinal choice models is introduced, combining a linear function with a nonlinear component modeled by deep neural networks to achieve both identifiability and interpretability. A two-step estimation algorithm is designed that maintains the order relations among outputs without relying on the parallelism assumption, making it appealing in practical applicability. The statistical properties of the smoothed MRC estimator are established under regular conditions, including identification, convergence rate, and minimax optimality, while allowing the number of categories to increase with sample size. Our theoretical results extend beyond ordinal choice models and apply to a broad range of generalized regression models. Extensive simulations demonstrate the superiority of the proposed method in classification accuracy and interpretability. Its effectiveness is further validated through applications to twelve benchmark datasets and an online education dataset.