A stopping rule for the Robbins-Monro method
type: Item
instance of: scholarly article
title: A stopping rule for the Robbins-Monro method
zbMATH Open document ID: 0687.62068
DOI: 10.1007/BF00939741
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: A stopping rule for the multi-dimensional Robbins-Monro stochastic approximation method is developed. Both moving average and stationary \(\phi\)-mixing type of correlated noise processes are treated. Sequentially determined confidence ellipsoids are constructed to fulfill the goal for the determination of the stopping rule. The limit behavior of the algorithm is investigated. It is shown that the stopped Robbins- Monro process is asymptotically normal. Such asymptotic normality is established by means of weak convergence methods.
Mathematics Subject Classification ID: 62L20
Mathematics Subject Classification ID: 62L15
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4126525
zbMATH Keywords: stationary phi-mixing
zbMATH Keywords: stopping rule
zbMATH Keywords: moving average
zbMATH Keywords: correlated noise processes
zbMATH Keywords: sequentially determined confidence ellipsoids
zbMATH Keywords: limit behavior
zbMATH Keywords: stopped Robbins-Monro process
zbMATH Keywords: asymptotic normality
zbMATH Keywords: weak convergence
author: G. Yin
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00939741
OpenAlex ID: W2053571628
description: scientific article; zbMATH DE number 4126525