Nonparametric estimation of composite functions
复合函数的非参数估计
We study the problem of nonparametric estimation of a multivariate function g: ℝd→ℝ that can be represented as a composition of two unknown smooth functions f: ℝ→ℝ and G: ℝd→ℝ. We suppose that f and G belong to known smoothness classes of functions, with smoothness γ and β, respectively. We obtain the full description of minimax rates of estimation of g in terms of γ and β, and propose rate-optimal estimators for the sup-norm loss. For the construction of such estimators, we…