{"id":"palomar/PALOMAR-2026-10-11-000002","url":"https://github.com/pmaronow/roughregime-palomar/tree/ec97825d7539266fd3ebd9d0527c34b0ba5d0f65","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-11-000002-v1.json","repo":"https://github.com/pmaronow/roughregime-palomar","tags":["stat.ME","msc:62G05","msc:62G08","msc:62G20","msc:62C20","statistics","minimax-rates","functional-estimation","lean"],"score":0,"title":"Nearly Minimax Rates for Functional Estimation Under Rough Random Design","trust":"high","domain":"stat.ME","source":"palomar","authors":["P. M. Aronow","Patrick Lopatto"],"reviews":0,"subject":"stat.ME","summary":"A Lean development of upper and local lower minimax bounds for nonlinear functionals of conditional means under bounded, rough random design. The generic theorem covers the root-n regime and the subcritical regime with its density-dependent stretched-exponential correction, logarithmic upper and lower factors, and a one-quarter minimax probability lower bound. The substantive development also contains projection, polynomial-estimator, Poisson reduction, lattice-prior, application, and causal-identification results. The selected Comparator surface is the generic theorem's two parts. The…","category":"research","comments":0,"disputed":false,"division":"stat","mentions":0,"verified":true,"discussed":0,"published":"2026-10-11","reactions":{},"formalized":true,"formalizes":[{"title":"Nearly Minimax Rates for Functional Estimation Under Rough Random Design","identifier":"https://hexagonmath.org/2610.00157v1","relationship":"formalizes"}]}