Asymptotic properties of neural network sieve estimators
Asymptotic properties of neural network sieve estimators
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DOI：
10.1080/10485252.2023.2209218
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发表时间：
2019-06
影响因子：
1.2
通讯作者：
Xiaoxi Shen;Chang Jiang;Lyudamila Sakhanenko;Q. Lu
中科院分区：
文献类型：
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作者：
Xiaoxi Shen;Chang Jiang;Lyudamila Sakhanenko;Q. Lu
神经网络已经成为机器学习和人工智能中最常用的方法之一。由于通用逼近定理，具有一个隐藏层的神经网络可以逼近紧支撑上的任何连续函数，只要隐藏单元的数量足够大。从统计学上讲，神经网络可以归类为非线性回归框架。然而，如果我们考虑它的参数，由于参数的不可识别性，这是很难得到它的渐近性质。相反，我们考虑在非参数回归框架的估计问题，并使用筛估计的结果建立的一致性，收敛速度和渐近正态性的神经网络估计。我们还通过模拟说明了理论的有效性。
Neural networks have become one of the most popularly used methods in machine learning and artificial intelligence. Due to the universal approximation theorem, a neural network with one hidden layer can approximate any continuous function on compact support as long as the number of hidden units is sufficiently large. Statistically, a neural network can be classified into a nonlinear regression framework. However, if we consider it parametrically, due to the unidentifiability of the parameters, it is difficult to derive its asymptotic properties. Instead, we consider the estimation problem in a nonparametric regression framework and use the results from sieve estimation to establish the consistency, the rates of convergence and the asymptotic normality of the neural network estimators. We also illustrate the validity of the theories via simulations.