Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks

Adams, 1975 Billingsley, 1979 Cybenko, 1989, Approximation by superpositions of a sigmodial function, 2, 303 Dugundji, 1966 Dym, 1972 Edmunds, 1977, Fourier approximations and embeddings in Sobolev space, Dissertationes Mathematicae, 145, 1 Elbadawi, 1983, An elastivity can be estimated consistently without a priori knowledge of functional form, Econometrica, 51, 1731, 10.2307/1912114 Funahashi, 1989, On the approximate realization of continuous mappings by neural networks, Neural Networks, 2, 183, 10.1016/0893-6080(89)90003-8 Gallant, 1987, Identification and consistency in semi-non-parametric regression, Vol. 1, 145 Gallant, 1989, On learning the derivatives of an unknown mapping with multilayer feedforward networks, UCSD Department of Economics Discussion Paper 89-53 Gilstrap, 1989, A general explanation and interrogation system for neural networks. Poster Presentation Halmos, 1974 hecht-Nielsen, 1989, Theory of the back-propagation neural network, I:593 Hornik, 1989, Multilayer feedforward networks are universal approximators, Neural Networks, 2, 359, 10.1016/0893-6080(89)90020-8 Irie, 1988, Capabilities of three-layered perceptrons, I:641 Jordan, 1989, Generic constraints on underspecified target trajectories, I:217 Kufner, 1980 Kufner, 1987 Lapedes, 1987, Nonlinear signal processing using neural networks: Prediction and system modeling Llavona, 1979, Approximations of differentiable functions, 197 Maz'ja, 1985 Schwartz, 1950 Showalter, 1977 Stinchcombe, 1989, Universal approximation using feedforward networks with non-sigmoid hidden layer activation functions, I:613 Ullah, 1988, Non-parametric estimation of econometric functionals, Canadian Journal of Economics, 21, 625, 10.2307/135443 Varian, 1978 Vinod, 1985, Flexible production function estimation by non-parametric kernel estimators