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September, 1976 An Application of a Theorem of Robbins and Siegmund
Dan Anbar
Ann. Statist. 4(5): 1018-1021 (September, 1976). DOI: 10.1214/aos/1176343602


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.


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Dan Anbar. "An Application of a Theorem of Robbins and Siegmund." Ann. Statist. 4 (5) 1018 - 1021, September, 1976.


Published: September, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0345.62069
MathSciNet: MR413390
Digital Object Identifier: 10.1214/aos/1176343602

Primary: 62L20
Secondary: 60G99

Keywords: almost supermartingale convergence theorem , Nonlinear regression , stochastic approximation

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 5 • September, 1976
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