Improved Rates and Asymptotic Normality for Nonparametric Neural Network Estimators (1997)
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BibTeX
@MISC{Chen97improvedrates,
author = {Xiaohong Chen and Halbert White},
title = {Improved Rates and Asymptotic Normality for Nonparametric Neural Network Estimators},
year = {1997}
}
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Abstract
Barron (1993) obtained a deterministic approximation rate (in L2-norm) of r-m for a class of single hid- den layer feedforward artificial neural networks (ANN) with r hidden units and sigmoid activation func- tions when the target function satisfies certain smoothness conditions. Hornik, Stinchcombe, White, and Auer (HSWA, 1994) extended Barron's result to a class of ANNs with possibly non-sigmoid activation approximating the target function and its derivatives simultaneously. Recently Makovoz (1996) obtained an improved degree of approximation rate r-o+/a for Barron's ANNs with sigmoid activation func- tion where d is the dimension of the domain of the target function.
