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

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  • Chen Xiaohong

    (Department of Economics, London School of Economics & Political Science)

  • White Halbert

    ()
    (Department of Economics, University of California, San Diego)

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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Bibliographic Info

Article provided by De Gruyter in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 6 (2002)
Issue (Month): 1 (April)
Pages: 1-55

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Handle: RePEc:bpj:sndecm:v:6:y:2002:i:1:n:1

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  1. V. Crawford, 2010. "Adaptive Dynamics in Coordination Games," Levine's Working Paper Archive 404, David K. Levine.
  2. Shwartz, Adam & Berman, Nadav, 1989. "Abstract stochastic approximations and applications," Stochastic Processes and their Applications, Elsevier, vol. 31(1), pages 133-149, March.
  3. Chen, Xiaohong & White, Halbert, 1998. "Nonparametric Adaptive Learning with Feedback," Journal of Economic Theory, Elsevier, vol. 82(1), pages 190-222, September.
  4. Chen, Xiaohong & White, Halbert, 1996. "Laws of Large Numbers for Hilbert Space-Valued Mixingales with Applications," Econometric Theory, Cambridge University Press, vol. 12(02), pages 284-304, June.
  5. Chen, Xiaohong & White, Halbert, 1998. "Central Limit And Functional Central Limit Theorems For Hilbert-Valued Dependent Heterogeneous Arrays With Applications," Econometric Theory, Cambridge University Press, vol. 14(02), pages 260-284, April.
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Cited by:
  1. Felipe Perez-Marti, 2000. "Private Experience in Adaptive Learning Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 283-310, April.

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