Session: Alumni Session

Date & Time: Saturday, May 23 — 1:30 PM–3:00 PM

Talk Title

Neyman-Orthogonal Comparison of Regression Functions

Abstract

Testing the equality of regression functions across two populations is fundamental for assessing whether regression relationships generalize across populations (external validity), whether different populations exhibit distinct response mechanisms (treatment heterogeneity), and whether regression structures remain stable across environments or regimes (regime stability). Classical residual-based procedures deteriorate in high dimensions and are not well suited to modern machine learning estimators.

We develop a framework that recasts two-sample regression comparison as a Neyman-orthogonal conditional moment restriction on pooled data, and constructs a test based on the dual norm of its representer in a reproducing kernel Hilbert space. The resulting statistic admits a closed-form quadratic representation and is calibrated using an empirically centered Gaussian multiplier bootstrap. Under the null hypothesis, we establish a finite-sample Kolmogorov distance bound to a Gaussian limit, prove non-asymptotic validity of the bootstrap, derive lower bounds on power against local alternatives, and show minimax optimality of the proposed test. For modern overparameterized learners such as neural networks, we additionally propose a novel k-fold cross-fitted statistic inspired by the proposed framework. Simulation studies and a real data application illustrate the utility of the proposed methods. This talk is based on joint work with Dr. Ao Sun, postdoctoral scholar at USC.