Confidence Intervals in Adaptive Nonparametric Estimation of Regression

Confidence intervals for the asymptotically optimal adaptive nonparametric estimates of regression are constructed under the assumption that the errors of measurements satisfy the existence condition of the higher-order moments or the condition

$$ \mathbf P(|\xi_i|>u)\leq C_2\exp(-C_3 u^q),\quad u>0,\quad q>0. $$