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November, 1973 On Optimal Estimation Methods Using Stochastic Approximation Procedures
Dan Anbar
Ann. Statist. 1(6): 1175-1184 (November, 1973). DOI: 10.1214/aos/1176342565


The problem of estimating the zero of a regression function by means of Robbins Monro type of stochastic approximation procedures is discussed. Optimality of the procedures is defined in terms of asymptotic variance. The discussion is restricted to the case of identically distributed errors. In that case we suggest transforming the observed random variables in order to minimize the asymptotic variance of the estimators. The optimal transformation turns out to depend on the underlying distribution of the errors and on the slope of the regression function at the zero.


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Dan Anbar. "On Optimal Estimation Methods Using Stochastic Approximation Procedures." Ann. Statist. 1 (6) 1175 - 1184, November, 1973.


Published: November, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0277.62064
MathSciNet: MR351001
Digital Object Identifier: 10.1214/aos/1176342565

Keywords: asymptotic optimal sequential design , asymptotic optimality , Nonlinear regression , optimal estimation , Robbins-Monro , sequential design , slope of a regression function , stochastic approximation

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 6 • November, 1973
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