Minimax Rates Under Global Overlap Bounds

Abstract

This note presents minimax regression rates for Dorn (2026)’s weak overlap setting. I show that weak overlap degrades the effective outcome smoothness rate by a factor of 1 - 1 / gamma_0. The bulk of the note is a proof that the minimax sup-norm rate is equal to the minimax pointwise rate, without the usual polylogarithmic penalty. Intuitively, there cannot be too many points with too weak overlap locally without making overlap worse globally. Further, I show the minimax rate is achievable adaptively without knowing or directly estimating the degree of overlap weakness.