Kernel regression and radial basis function net: some theoretical studies

After building up some connections between the radial basis function (RBF) network and kernel regression estimator (KRE), the authors introduce several recent theoretical results on KRE. They show that KRE can not only be used as a neural network model, but can also provide new results on the theoretical analysis of an RBF net in terms of the ability of approximation, the rate of convergence, and the size of the receptive field of the radial basis function. These results are quite useful for further theoretical studies on the RBF as well as in guiding the design of the RBF net in practice.<>