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

Xiaohong Chen () and Halbert White

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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Citations: View citations in EconPapers (8)

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Journal Article: Asymptotic Properties of Some Projection-based Robbins-Monro Procedures in a Hilbert Space (2002)
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