Asymptotic Properties of Some Projection-based Robbins-Monro Procedures in a Hilbert Space
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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Volume (Year): 6 (2002)
Issue (Month): 1 (April)
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- Chen, Xiaohong & White, Halbert, 1998. "Nonparametric Adaptive Learning with Feedback," Journal of Economic Theory, Elsevier, vol. 82(1), pages 190-222, September.
- 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.
- V. Crawford, 2010.
"Adaptive Dynamics in Coordination Games,"
Levine's Working Paper Archive
404, David K. Levine.
- Shwartz, Adam & Berman, Nadav, 1989. "Abstract stochastic approximations and applications," Stochastic Processes and their Applications, Elsevier, vol. 31(1), pages 133-149, March.
- 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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