On integer stochastic approximation

Václav Dupač; Ulrich Herkenrath

Aplikace matematiky (1984)

  • Volume: 29, Issue: 5, page 372-383
  • ISSN: 0862-7940

Abstract

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Let M : 𝐑 𝐑 be observable, with experimental errors, at integer points only; unknown elsewhere. Iterative nonparametric procedures for finding the zero point of M are called procedures of integer stochastic approximation. Three types of such procedures (Derman’s, Mukerjee’s and the authors’) are described and compared. A two-dimensional analogue of the third approach is proposed and investigated; its generalization to higher dimensions is conjectured.

How to cite

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Dupač, Václav, and Herkenrath, Ulrich. "On integer stochastic approximation." Aplikace matematiky 29.5 (1984): 372-383. <http://eudml.org/doc/15368>.

@article{Dupač1984,
abstract = {Let $M : \mathbf \{R\} \rightarrow \mathbf \{R\}$ be observable, with experimental errors, at integer points only; unknown elsewhere. Iterative nonparametric procedures for finding the zero point of $M$ are called procedures of integer stochastic approximation. Three types of such procedures (Derman’s, Mukerjee’s and the authors’) are described and compared. A two-dimensional analogue of the third approach is proposed and investigated; its generalization to higher dimensions is conjectured.},
author = {Dupač, Václav, Herkenrath, Ulrich},
journal = {Aplikace matematiky},
keywords = {nonparametric procedures; Robbins-Monro type procedure; integer stochastic approximation; nonparametric procedures; Robbins-Monro type procedure; integer stochastic approximation},
language = {eng},
number = {5},
pages = {372-383},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On integer stochastic approximation},
url = {http://eudml.org/doc/15368},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Dupač, Václav
AU - Herkenrath, Ulrich
TI - On integer stochastic approximation
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 5
SP - 372
EP - 383
AB - Let $M : \mathbf {R} \rightarrow \mathbf {R}$ be observable, with experimental errors, at integer points only; unknown elsewhere. Iterative nonparametric procedures for finding the zero point of $M$ are called procedures of integer stochastic approximation. Three types of such procedures (Derman’s, Mukerjee’s and the authors’) are described and compared. A two-dimensional analogue of the third approach is proposed and investigated; its generalization to higher dimensions is conjectured.
LA - eng
KW - nonparametric procedures; Robbins-Monro type procedure; integer stochastic approximation; nonparametric procedures; Robbins-Monro type procedure; integer stochastic approximation
UR - http://eudml.org/doc/15368
ER -

References

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  1. C. Derman, 10.1214/aoms/1177706895, Ann. Math. Statist. 28 (1957), 795-797. (1957) Zbl0084.14801MR0090956DOI10.1214/aoms/1177706895
  2. V. Dupač U. Herkenrath, 10.1080/07474948208836002, Comm. Statist.-Sequential Analysis 1 (1982), 1 - 26. (1982) Zbl0483.62071MR0667411DOI10.1080/07474948208836002
  3. U. Herkenrath, 10.1007/BF02056924, Metrika 30 (1983), 195 - 210. (1983) Zbl0519.62066MR0726019DOI10.1007/BF02056924
  4. A. Kirchen, Überlegungen zur eindimersionalen stochastischen Approximation, Diploma work. University of Bonn, Í982. 
  5. H. G. Mukerjee, 10.1214/aos/1176345581, Ann. Statist. 9 (1981), 1020-1025. (1981) Zbl0478.62069MR0628757DOI10.1214/aos/1176345581
  6. M. B. Neveľson R. Z. Has'minskij, Stochastic Approximation and Recursive Estimation, Translation of Mathem. Monographs, vol. 47, Amer. Mathem. Soc., Providence, 1976. (Russian original, Nauka, Moskva 1982.) (1976) 

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