Article
Full entry |
PDF
(1.6 MB)
Feedback
PDF
(1.6 MB)
Feedback
Keywords:
nonparametric procedures; Robbins-Monro type procedure; integer stochastic approximation
nonparametric procedures; Robbins-Monro type procedure; integer stochastic approximation
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.
References:
[1] C. Derman: Non-parametric up-and-down experimentation. Ann. Math. Statist. 28 (1957), 795-797. DOI 10.1214/aoms/1177706895 | MR 0090956 | Zbl 0084.14801
[2] V. Dupač U. Herkenrath: Stochastic approximation on a discrete set and the multiarmed bandit problem. Comm. Statist.-Sequential Analysis 1 (1982), 1 - 26. DOI 10.1080/07474948208836002 | MR 0667411
[3] U. Herkenrath: The N-armed bandit with unimodal structure. Metrika 30 (1983), 195 - 210. DOI 10.1007/BF02056924 | MR 0726019 | Zbl 0519.62066
[4] A. Kirchen: Überlegungen zur eindimersionalen stochastischen Approximation. Diploma work. University of Bonn, Í982.
[5] H. G. Mukerjee: A stochastic approximation by observations on a discrete lattice using isotonic regression. Ann. Statist. 9 (1981), 1020-1025. DOI 10.1214/aos/1176345581 | MR 0628757 | Zbl 0478.62069
[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.)
Search
Partner of
