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September, 1952 Stochastic Estimation of the Maximum of a Regression Function
J. Kiefer, J. Wolfowitz
Ann. Math. Statist. 23(3): 462-466 (September, 1952). DOI: 10.1214/aoms/1177729392

Abstract

Let $M(x)$ be a regression function which has a maximum at the unknown point $\theta. M(x)$ is itself unknown to the statistician who, however, can take observations at any level $x$. This paper gives a scheme whereby, starting from an arbitrary point $x_1$, one obtains successively $x_2, x_3, \cdots$ such that $x_n$ converges to $\theta$ in probability as $n \rightarrow \infty$.

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J. Kiefer. J. Wolfowitz. "Stochastic Estimation of the Maximum of a Regression Function." Ann. Math. Statist. 23 (3) 462 - 466, September, 1952. https://doi.org/10.1214/aoms/1177729392

Information

Published: September, 1952
First available in Project Euclid: 28 April 2007

zbMATH: 0049.36601
MathSciNet: MR50243
Digital Object Identifier: 10.1214/aoms/1177729392

Rights: Copyright © 1952 Institute of Mathematical Statistics

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Vol.23 • No. 3 • September, 1952
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