标题： 速率最优估计对于具有未知链接函数的一般非参数回归模型 显示英文标题

标题： Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions

摘要： 本文讨论了一个非参数回归模型，该模型自然推广了神经网络模型。 该模型基于有限数量的一维变换，并且可以以一维收敛速度进行估计。 该模型包含具有未知连接函数的广义可加模型作为特例。 对于这种情况，证明了通过求解惩罚最小二乘准则的平滑样条，可以以最优速率估计可加成分和连接函数。 显示英文摘要

摘要： This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of convergence. The model contains the generalized additive model with unknown link function as a special case. For this case, it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a penalized least squares criterion.