Asymptotic Properties of Some Projection-based Robbins-Monro Procedures in a Hilbert Space
AbstractLet H be an infinite-dimentional real separable Hilbert space. Given an unknown mapping M : H (arrow) H that can only be observed with noise, we consider two modified Robbins-Monro procedures to estimate the zero point (theta) (subscript 0) ? 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, (theta)-dependent error processes.
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Bibliographic InfoPaper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt4z4380t7.
Date of creation: 01 Jan 2002
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Other versions of this item:
- Chen Xiaohong & White Halbert, 2002. "Asymptotic Properties of Some Projection-based Robbins-Monro Procedures in a Hilbert Space," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(1), pages 1-55, April.
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
- C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
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- Shwartz, Adam & Berman, Nadav, 1989. "Abstract stochastic approximations and applications," Stochastic Processes and their Applications, Elsevier, vol. 31(1), pages 133-149, March.
- V. Crawford, 2010.
"Adaptive Dynamics in Coordination Games,"
Levine's Working Paper Archive
404, David K. Levine.
- 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.
- 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.
- Chen, Xiaohong & White, Halbert, 1998. "Nonparametric Adaptive Learning with Feedback," Journal of Economic Theory, Elsevier, vol. 82(1), pages 190-222, September.
- 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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