Accomplishment Based Renewal For Research in Specification Testing, Nonparametric Estimation and Neural Networks

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Artificial neural networks (ANN's) are a rich and interesting class of nonlinear models developed recently by cognitive scientists. Although inspired by certain features of the neural architecture of the brain, these models have considerable potential for use in econometrics and economics because of their simplicity and great flexibility. Specifically, ANN models show promise as the basis for nonparmetric estimation and for specification testing because of their ability to approximate arbitrary elements of general function spaces to arbitrary accuracy. Under previous NSF grants, this project focused on establishing the mathematical and statistical foundations necessary for using ANN models in nonparametric estimation and specification testing. The research proposed in this accomplishment based renewal is to continue development of these foundations, to establish properties of ANN- based nonparametric estimators, and to apply the resulting theory to construct model specification tests. The areas in which mathematical and statistical theory will be pursued are two. The first area is the establishment of degree of approximation results for ANN models in Sobolev spaces. The second area is to obtain central limit theorems and invariance principles for random elements constructed as partial sums of a dependent process (specifically, a mixingale process) in a Hilbert space. The application areas make direct use of the proposed theoretical results to model learning by economic agents.