Stochastic approximation from ergodic sample for linear regression

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

Robbins-Monro stochastic approximation procedure {Mathematical expression} is used to solve the linear equation Ax=y in Hilbert space, where yn and An are estimators such that their arithmetic means converge to y and A, respectively. Under some additional conditions it is shown that Xn goes to the unique solution of this equation.

Original languageEnglish
Pages (from-to)47-55
Number of pages9
JournalZeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete
Volume54
Issue number1
DOIs
Publication statusPublished - Jan 1980

Fingerprint

Stochastic Approximation
Linear regression
Unique Solution
Linear equation
Hilbert space
Converge
Estimator
Stochastic approximation

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

Stochastic approximation from ergodic sample for linear regression. / Györfi, L.

In: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, Vol. 54, No. 1, 01.1980, p. 47-55.

Research output: Contribution to journalArticle

@article{c12b29df42054108a1cd5bf1a7c67915,
title = "Stochastic approximation from ergodic sample for linear regression",
abstract = "Robbins-Monro stochastic approximation procedure {Mathematical expression} is used to solve the linear equation Ax=y in Hilbert space, where yn and An are estimators such that their arithmetic means converge to y and A, respectively. Under some additional conditions it is shown that Xn goes to the unique solution of this equation.",
author = "L. Gy{\"o}rfi",
year = "1980",
month = "1",
doi = "10.1007/BF00535352",
language = "English",
volume = "54",
pages = "47--55",
journal = "Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete",
issn = "0178-8051",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - Stochastic approximation from ergodic sample for linear regression

AU - Györfi, L.

PY - 1980/1

Y1 - 1980/1

N2 - Robbins-Monro stochastic approximation procedure {Mathematical expression} is used to solve the linear equation Ax=y in Hilbert space, where yn and An are estimators such that their arithmetic means converge to y and A, respectively. Under some additional conditions it is shown that Xn goes to the unique solution of this equation.

AB - Robbins-Monro stochastic approximation procedure {Mathematical expression} is used to solve the linear equation Ax=y in Hilbert space, where yn and An are estimators such that their arithmetic means converge to y and A, respectively. Under some additional conditions it is shown that Xn goes to the unique solution of this equation.

UR - http://www.scopus.com/inward/record.url?scp=0008738007&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0008738007&partnerID=8YFLogxK

U2 - 10.1007/BF00535352

DO - 10.1007/BF00535352

M3 - Article

VL - 54

SP - 47

EP - 55

JO - Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

JF - Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

SN - 0178-8051

IS - 1

ER -