Asymptotic uniform confidence bands are constructed for a multivariate nonparametric regression model with heteroscedastic noise, employing histogram estimators under flexible partition conditions. The construction is especially applicable to unsmooth regression functions of Hölder regularity less than one. While the radius of the confidence bands could be approximated via the Gumbel distribution, our construction does not depend on an extreme value distribution, but instead can be explicitly calculated for the chosen partition.

翻译：针对具有异方差噪声的多元非参数回归模型，本文在灵活划分条件下采用直方图估计量构建了渐近一致置信带。该构建方法特别适用于Hölder正则性小于1的非光滑回归函数。虽然置信带半径可通过Gumbel分布近似计算，但我们的构建方法不依赖于极值分布，而是能够针对所选划分进行显式计算。