Nonparametric Uniform Inference in Binary Classification and Policy Values

Abstract

We develop methods for nonparametric uniform inference in cost-sensitive binary classification, a framework that encompasses maximum score estimation, predicting utility maximizing actions, and policy learning. These problems are well known for slow convergence rates and non-standard limiting behavior, even under point identified parametric frameworks. In nonparametric settings, they may further suffer from failures of identification. To address these challenges, we introduce a strictly convex surrogate loss that point-identifies a representative nonparametric policy function. We then estimate this representative policy function to conduct inference on both the optimal classification policy and the optimal policy value. This approach enables Gaussian inference, substantially simplifying empirical implementation relative to working directly with the original classification problem. In particular, we establish root-$n$ asymptotic normality for the optimal policy value and derive a Gaussian approximation for the optimal classification policy at the standard nonparametric rate. Extensive simulation studies corroborate the theoretical findings. We apply our method to the National JTPA Study to conduct inference on the optimal treatment assignment policy and its associated welfare.