Consistency of stochastic approximation algorithm with quasi-associated random errors

Idir Arab and Abdelnasser Dahmani

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 23, 6883-6890

Abstract: Many mathematical and physical problems are led to find a root of a real function f. This kind of equation is an inverse problem and it is difficult to solve it. Especially in engineering sciences, the analytical expression of the function f is unknown to the experimenter, but it can be measured at each point xk with M(xk) as expected value and induced error ξk. The aim is to approximate the unique root θ under some assumptions on the function f and errors ξk. We use a stochastic approximation algorithm that constructs a sequence (xk)k ⩾ 1. We establish the almost complete convergence of the sequence (xk)k to the exact root θ by considering the errors (ξk)k quasi-associated and we illustrate the method by numerical examples to show its efficiency.

Date: 2016
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2014.968737 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:45:y:2016:i:23:p:6883-6890

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2014.968737

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().