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

Xiaohong Chen and Halbert White
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Xiaohong Chen: Yale University

No 2002-07, University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego

Abstract: Let 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.

Keywords: Hilbert Space. (search for similar items in EconPapers)
Date: 2002-01-01
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Related works:
Working Paper: Asymptotic Properties of Some Projection-based Robins-Monro Procedures in a Hilbert Space (1992)
Journal Article: Asymptotic Properties of Some Projection-based Robbins-Monro Procedures in a Hilbert Space (2002)
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Persistent link: http://EconPapers.repec.org/RePEc:cdl:ucsdec:2002-07

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