Regression smoothing parameters that are not far from their optimum
Regression smoothing parameters that are not far from their optimum
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DOI：
10.1080/01621459.1992.10475196
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发表时间：
1992
影响因子：
3.7
通讯作者：
W. Härdle;P. Hall;J. Marron
中科院分区：
文献类型：
--
作者：
W. Härdle;P. Hall;J. Marron
摘要众所周知，基于交叉验证的数据驱动回归平滑参数预测及相关方法收敛速度慢。在之前的文章中，我们证明了这个速率可以慢到n-1/10;也就是说，对于优化平均平方误差的带宽预测0，n 1/10（预测-预测0）/预测0趋于渐近正态分布。在这篇文章中，我们考虑均方误差最优带宽h 0。这个（非随机）平滑参数可以更快地近似。我们使用双重平滑的技术表明，有一个预测，在一定条件下，n 1/2（预测-h 0）/h 0趋于渐近正态分布。
Abstract It is well known that data-driven regression smoothing parameters ħ based on cross-validation and related methods exhibit a slow rate of convergence to their optimum. In an earlier article we showed that this rate can be as slow as n –1/10; that is, for a bandwidth ħ 0 optimizing the averaged squared error, n 1/10 (ħ — ħ 0)/ħ 0 tends to an asymptotic normal distribution. In this article we consider mean averaged squared error optimal bandwidths h 0. This (nonrandom) smoothing parameter can be approximated much faster. We use the technique of double smoothing to show that there is an ħ such that, under certain conditions, n 1/2(ħ − h 0)/h 0 tends to an asymptotic normal distribution.