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We give conditions ensuring that multilayer jeedJorward networks with as Jew as a single hidden layer and an appropriately smooth hidden layer activation fimction are capable of arbitrarily accurate approximation to an arbitrao' function and its derivatives. In fact, these networks can approximate functions that are not dtifferentiable in the classical(More)
The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric t, and neither dominates in experiments. This topological uniication allows us to greatly extend the nuisance parameter approach. How and why the nuisance(More)
K.M. Hornik, M. Stinchcombe, and H. White (Univ. of California at San Diego, Dept. of Economics Discussion Paper, June 1988; to appear in Neural Networks) showed that multilayer feedforward networks with as few as one hidden layer, no squashing at the output layer, and arbitrary sigmoid activation function at the hidden layer are universal approximators:(More)
Normal form games are nearly compact and continuous (NCC) if they can be understood as games played on strategy spaces that are dense subsets of the strategy spaces of larger compact games with jointly continuous payoffs. There are intrinsic algebraic, measure theoretic, functional analysis, and finite approximabil-ity characterizations of NCC games. NCC(More)