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

Xiaohong Chen () and Halbert White

Studies in Nonlinear Dynamics & Econometrics, 2002, vol. 6, issue 1, 55

Abstract: 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.

Date: 2002
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DOI: 10.2202/1558-3708.1000

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