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

U of California, Economics Working Paper No. 2002-07

77 Pages Posted: 5 Jun 2002

See all articles by Xiaohong Chen

Xiaohong Chen

Yale University - Cowles Foundation

Halbert L. White, Jr.

University of California, San Diego (UCSD) - Department of Economics

Date Written: January 2002

Abstract

Let H be an infinite-dimensional real separable Hilbert space. Given an unknown mapping M : H 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 mix-ingale, -dependent error processes.

Keywords: Recursive Estimation, Non-Parametric Estimation, Hilbert Space, Generalized Method of Moments

JEL Classification: C14

Suggested Citation

Chen, Xiaohong and White, Halbert L., Asymptotic Properties of Some Projection-Based Robbins-Monro Procedures in a Hilbert Space (January 2002). U of California, Economics Working Paper No. 2002-07, Available at SSRN: https://ssrn.com/abstract=313836 or http://dx.doi.org/10.2139/ssrn.313836

Xiaohong Chen (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Halbert L. White

University of California, San Diego (UCSD) - Department of Economics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
858-534-3502 (Phone)
858-534-7040 (Fax)

HOME PAGE: http://www.econ.ucsd.edu/~mbacci/white/

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