Local convergence theorems for adaptive stochastic approximation schemes
- 1 July 1979
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 76 (7) , 3065-3067
- https://doi.org/10.1073/pnas.76.7.3065
Abstract
For the regression model y = M(x) + epsilon, adaptive stochastic approximation schemes of the form x(n+1) = x(n) - y(n)/(nb(n)) for choosing the levels x(1),x(2),... at which y(1),y(2),... are observed converge with probability 1 to the unknown root theta of the regression function M(x). Certain local convergence theorems that relate the convergence rate of x(n) - theta to the limiting behavior of the random variables b(n) are established.Keywords
This publication has 1 reference indexed in Scilit:
- Limit theorems for weighted sums and stochastic approximation processesProceedings of the National Academy of Sciences, 1978