Optimal estimation in additive regression models
Optimal estimation in additive regression models
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DOI：
10.3150/bj/1145993975
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发表时间：
2006-04-01
期刊：
影响因子：
1.5
通讯作者：
Mammen, E
中科院分区：
文献类型：
--
作者：
Horowitz, J;Klemelä, J;Mammen, E
本文涉及非参数加法回归模型中加法成分的最优估计。本文考虑了几种不同的平滑方法，包括核、局部多项式、平滑样条和正交序列。结果表明，从一阶近似值来看，每个加法成分的估计结果与已知其他成分的估计结果一样好。利用这一结果可以说明，在加法模型中，渐近最优最小率和常数与具有一个分量的非参数回归模型中的渐近最优最小率和常数相同。
This paper is concerned with optimal estimation of the additive components of a nonparametric, additive regression model. Several different smoothing methods are considered, including kernels, local polynomials, smoothing splines and orthogonal series. It is shown that, asymptotically up to first order, each additive component, can be estimated as well as it could be if the other components were known. This result is used to show that in additive models the asymptotically optimal minimax rates and constants are the same as they are in nonparametric regression models with one component.