A stopped stochastic approximation algorithm
type: Item
instance of: scholarly article
title: A stopped stochastic approximation algorithm
zbMATH Open document ID: 0652.62082
DOI: 10.1016/0167-6911(88)90083-7
published in: Systems \& Control Letters
publication date: 1988-01-01T00:00:00Z
review text: A stopping time problem for a multidimensional Robbins-Monro stochastic approximation procedure is studied. The stopping rule is determined such that the procedure will be terminated if the unknown parameter \(\theta\) (the root of the regression function) is inside a desired ellipsoidal confidence region with high probability. Some usual assumptions are supposed to be valid for this stochastic approximation procedure. The noise processes are supposed to fulfill a condition of martingale type but not to be necessarily independent. The stopped process is then shown to be asymptotically normal by means of weak convergence methods. The construction of the desired confidence ellipsoids is described.
reviewed by: T.Fiala
Mathematics Subject Classification ID: 62L20
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 62L15
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4064312
zbMATH Keywords: multidimensional Robbins-Monro stochastic approximation procedure
zbMATH Keywords: root of the regression function
zbMATH Keywords: ellipsoidal confidence region
zbMATH Keywords: weak convergence
author: G. Yin
MaRDI profile type: Publication
full work available at URL: 0167-6911(88)90083-7
OpenAlex ID: W1986077525
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description: scientific article; zbMATH DE number 4064312