| Title:
|
On integer stochastic approximation (English) |
| Author:
|
Dupač, Václav |
| Author:
|
Herkenrath, Ulrich |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
29 |
| Issue:
|
5 |
| Year:
|
1984 |
| Pages:
|
372-383 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $M : \bold R \rightarrow \bold R$ 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. (English) |
| Keyword:
|
nonparametric procedures |
| Keyword:
|
Robbins-Monro type procedure |
| Keyword:
|
integer stochastic approximation |
| MSC:
|
62L20 |
| idZBL:
|
Zbl 0589.62074 |
| idMR:
|
MR0772272 |
| DOI:
|
10.21136/AM.1984.104107 |
| . |
| Date available:
|
2008-05-20T18:25:50Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104107 |
| . |
| Reference:
|
[1] C. Derman: Non-parametric up-and-down experimentation.Ann. Math. Statist. 28 (1957), 795-797. Zbl 0084.14801, MR 0090956, 10.1214/aoms/1177706895 |
| Reference:
|
[2] V. Dupač U. Herkenrath: Stochastic approximation on a discrete set and the multiarmed bandit problem.Comm. Statist.-Sequential Analysis 1 (1982), 1 - 26. MR 0667411, 10.1080/07474948208836002 |
| Reference:
|
[3] U. Herkenrath: The N-armed bandit with unimodal structure.Metrika 30 (1983), 195 - 210. Zbl 0519.62066, MR 0726019, 10.1007/BF02056924 |
| Reference:
|
[4] A. Kirchen: Überlegungen zur eindimersionalen stochastischen Approximation.Diploma work. University of Bonn, Í982. |
| Reference:
|
[5] H. G. Mukerjee: A stochastic approximation by observations on a discrete lattice using isotonic regression.Ann. Statist. 9 (1981), 1020-1025. Zbl 0478.62069, MR 0628757, 10.1214/aos/1176345581 |
| Reference:
|
[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.) |
| . |
