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Asymptotic Properties of Some Projection-based Robbins-Monro Procedures in a Hilbert Space

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Author Info
Xiaohong Chen (Department of Economics, London School of Economics & Political Science)
Halbert White (Department of Economics, University of California, San Diego)

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Abstract

Let H be an infinite-dimensional real separable Hilbert space. Given an unknown mapping M:H (r)H that can only be observed with noise, we consider two modified Robbins-Monro procedures to estimate the zero point ?o ( H of M. These procedures work in appropriate finite dimensional sub-spaces of growing dimension. Almost-sure convergence, functional central limit theorem (hence asymptotic normality), law of iterated logarithm (hence almost-sure loglog rate of convergence), and mean rate of convergence are obtained for Hilbert space-valued mixingale, (-dependent error processes.

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Publisher Info
Article provided by Berkeley Electronic Press in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 6 (2002)
Issue (Month): 1 ()
Pages: 1000-1000
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Handle: RePEc:bep:sndecm:6:2002:1:1000-1000

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Related research
Keywords: Nonparametric recursive moment estimations nonparametric learning procedures Hilbert-valued Robbins-Monro procedures Hilbert-valued Near Epoch Dependent processes convergence rate limiting distributions

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Pakes, Ariel & McGuire, Paul, 2001. "Stochastic Algorithms, Symmetric Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Econometrica, Econometric Society, vol. 69(5), pages 1261-81, September.
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  3. Chen, Xiaohong & White, Halbert, 1998. "Nonparametric Adaptive Learning with Feedback," Journal of Economic Theory, Elsevier, vol. 82(1), pages 190-222, September. [Downloadable!] (restricted)
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  4. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August. [Downloadable!] (restricted)
  5. Crawford, Vincent P, 1995. "Adaptive Dynamics in Coordination Games," Econometrica, Econometric Society, vol. 63(1), pages 103-43, January. [Downloadable!] (restricted)
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  6. Spear, Stephen E, 1989. "Learning Rational Expectations under Computability Constraints," Econometrica, Econometric Society, vol. 57(4), pages 889-910, July. [Downloadable!] (restricted)
  7. Evans, George W & Honkapohja, Seppo, 1995. "Local Convergence of Recursive Learning to Steady States and Cycles in Stochastic Nonlinear Models," Econometrica, Econometric Society, vol. 63(1), pages 195-206, January. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Felipe Perez, 1997. "Private Experience in Adaptive Learning Models," Levine's Working Paper Archive 1403, UCLA Department of Economics. [Downloadable!]
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