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Licensed Unlicensed Requires Authentication Published by De Gruyter April 1, 2002

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

  • Xiaohong Chen and Halbert White

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.

Published Online: 2002-4-1

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