Abstract
We establish the consistency of nonparametric conditional quantile estimators based on artificial neural networks. The results follow from general results on sieve estimation for dependent processes. We also show that conditional quantiles can be learned to any pre-specified accuracy using approximate rather than exact network optimization.
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Carroll, S.M. and B.W. Dickinson, (1989), “Construction of Neural Nets Using the Radon Transform,” in Proceedings of the International Joint Conference on Neural Networks, Washington, D.C., New York: IEEE Press, pp. I:607–I:611.
Cybenko, G. (1989), “Approximation by Superposition of a Sigmoid Function,” Mathematics of Control, Signals and Systems 2, 303–314.
Fulton, M., S. Subramanian and R. Carson (1987), “Estimating Fast Regression Quantiles Using a Modification of the Barrodale and Roberts L 1 Algorithm,” Department of Economics Discussion Paper 87-8, University of California, San Diego.
Funahashi, K. (1989), “On the Approximate Realization of Continuous Mappings by Neural Networks,” Neural Networks, 2, 183–192.
Geman, S. and C. Hwang (1982): “Nonparametric Maximum Likelihood Estimation by the Method of Sieves,” The Annals of Statistics 10, 401–414.
Goldberg, D. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison Wesley.
Grenander, U. (1981). Abstract Inference. New York: Wiley.
Hajek, B. (1985), “A Tutorial Survey of Theory and Applications of Simulated Annealing,” in Proceedings of the 24th IEEE Conference on Decision and Control, pp. 755–760.
Hecht-Nielsen, R. (1989), “Theory of the Back-Propagation Neural Network,” in Proceedings of the International Joint Conference on Neural Networks, Washington, D.C., New York: IEEE Press, pp. I: 593–I: 606.
Hornik, K. (1989), “Learning Capabilities of Multilayer Feedforward Networks,” Technische Universität Wien, technical report.
Hornik, K., M. Stinchcombe and H. White (1989), “Multilayer Feedforward Networks are Universal Approximators,” Neural Networks 2, 359–366.
Hornik, K., M. Stinchcombe and H. White (1990), “Universal Approximation of an Unknown Mapping and Its Derivatives,” Neural Networks 3, 551–560.
Holland, J. (1975). Adaptation in Natural and Artificial Systems. Ann Arbor: University of Michigan Press.
Koenker, R. and G. Basset(1978), “Regression Quantiles,” Econometrica 46, 33–55.
Rinnooy Kan, A.H.G., C.G.E. Boender and G. Th. Timmer (1985), “A Stochastic Approach to Global Optimization,” in K. Schittkowski, ed., Computational Mathematical Programming, NATO ASI Series, Vol. F15. Berlin: Springer-Verlag, pp. 281–308.
Rudin, W. (1974). Real and Complex Analysis. New York: McGraw Hill.
Stinchcombe, M. and H. White (1989), “Universal Approximation Using Feedforward Networks with Non-Sigmoid Hidden Layer Activation Functions,” in Proceedings of the International Joint Conference on Neural Networks, Washington, D.C., New York: IEEE Press, pp. I: 613–I: 617.
Stinchcombe, M. and H. White (1990), “Approximating and Learning Unknown Mappings Using Multilayer Feedforward Networks with Bounded Weights,” in Proceedings of the International Joint Conference on Neural Networks, San Diego. New York: IEEE Press, pp. III–7–15.
Stout, W.F. (1974). Almost Sure Convergence. New York: Academic Press.
White, H. (1989), “Learning in Artificial Neural Networks: A Statistical Perspective,” Neural Computation 1, 425–464.
White, H. (1990), “Connectionist Nonparametric Regression: Multilayer Feedforward Networks Can Learn Arbitrary Mappings,” Neural Networks 3, 535–550.
White, H. and J. Wooldridge (1991), “Some Results on Sieve Estimation with Dependent Observations,” in W. Barnett, J. Powell and G. Tauchen, eds., Nonparametric and Semi-Parametric Methods in Econometrics and Statistics. New York: Cambridge University Press, (to appear)
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© 1992 Springer-Verlag New York, Inc.
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White, H. (1992). Nonparametric Estimation of Conditional Quantiles Using Neural Networks. In: Page, C., LePage, R. (eds) Computing Science and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2856-1_25
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DOI: https://doi.org/10.1007/978-1-4612-2856-1_25
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97719-5
Online ISBN: 978-1-4612-2856-1
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