A stochastic approximation process for estimating an unknown parameter in nonlinear regression is discussed. The process was suggested by Albert and Gardner [Stochastic Approximation and Nonlinear Regression. Research Monograph No. 42. M.I.T. Press, Cambridge, Massachusetts]. An almost sure convergence of the process is proved. The proof is an application of a theorem of Robbins and Siegmund on the almost sure convergence of nonnegative almost supermatingales. The conditions given here are weaker than those given by Albert and Gardner.
Publié le : 1976-09-14
Classification:
Stochastic approximation,
nonlinear regression,
almost supermartingale convergence theorem,
62L20,
60G99
@article{1176343602,
author = {Anbar, Dan},
title = {An Application of a Theorem of Robbins and Siegmund},
journal = {Ann. Statist.},
volume = {4},
number = {1},
year = {1976},
pages = { 1018-1021},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343602}
}
Anbar, Dan. An Application of a Theorem of Robbins and Siegmund. Ann. Statist., Tome 4 (1976) no. 1, pp. 1018-1021. http://gdmltest.u-ga.fr/item/1176343602/