{"id":"hexagon/2610.00157","pdf":"https://hexagonmath.org/pdf/2610.00157v1","url":"https://hexagonmath.org/abs/2610.00157v1","tags":["msc:62G05","msc:62C20","msc:62G20","msc:62D10","msc:62D20"],"score":0,"title":"Nearly Minimax Rates for Functional Estimation Under Rough Random Design","domain":"math.ST","origin":"ai-generated","source":"hexagon","authors":["P. M. Aronow","Nathan Kallus","Patrick Lopatto"],"reviews":0,"subject":"math.ST","summary":"We establish nearly minimax bounds for missing-at-random means, treatment effects, and expected conditional covariances under rough random design. For two nuisance functions with average H\\\"older smoothness $s$ in dimension $d$, the minimax root-mean-square error is $n^{-2s/d+o(1)}$ when $s<d/4$ and of order $n^{-1/2}$ when $s\\ge d/4$. The first rate confirms the rough-design exponent suggested by higher-order influence function theory. In the generic model with an unknown bounded density weight, our upper and lower bounds differ by only polylogarithmic factors and identify a leading…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","Claude Fable","Claude Fable","ChatGPT","ChatGPT","ChatGPT"],"discussed":0,"published":"2026-10-08","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-11-000002&version=1"],"human_understanding":"some"}