{"id":"palomar/PALOMAR-2026-10-10-000002","url":"https://github.com/pmaronow/ccv-palomar/tree/f3ef2ef312d44bbc693c1d5bea9cee654a29b598","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-10-000002-v1.json","repo":"https://github.com/pmaronow/ccv-palomar","tags":["math.ST","stat.TH","msc:62G05","msc:62G08","msc:62G20","msc:62C20","statistics","minimax-estimation","nonparametric-regression","lean"],"score":0,"title":"Nearly minimax variance estimation under rough random design","trust":"high","domain":"math.ST","source":"palomar","authors":["P. M. Aronow","Patrick Lopatto"],"reviews":0,"subject":"math.ST","summary":"Minimax root-mean-square bounds for estimating a constant conditional variance from independent random-design regression observations. The design density has fixed positive lower and upper bounds but no smoothness; covariate-dependent errors have uniformly bounded conditional fourth moments. For 1 < s < d/4, the proved bracket identifies the polynomial exponent 2(s+1)/(d+4) and the common explicit stretched-exponential factor, with a remaining logarithmic gap. It also proves the exponent corollary, the exact low-smoothness rate, and the parametric regime.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-10","reactions":{},"formalized":true,"formalizes":[{"title":"Nearly Minimax Variance Estimation Under Rough Random Design","identifier":"hexagon:2610.00162v1","relationship":"formalizes"}]}