The Annals of Mathematical Statistics

Stochastic Estimation of the Maximum of a Regression Function

J. Kiefer and J. Wolfowitz

Full-text: Open access

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 $n \rightarrow \infty$.

Article information

Source
Ann. Math. Statist. Volume 23, Number 3 (1952), 462-466.

Dates
First available: 28 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoms/1177729392

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoms/1177729392

Mathematical Reviews number (MathSciNet)
MR50243

Zentralblatt MATH identifier
0049.36601

Citation

Kiefer, J.; Wolfowitz, J. Stochastic Estimation of the Maximum of a Regression Function. The Annals of Mathematical Statistics 23 (1952), no. 3, 462--466. doi:10.1214/aoms/1177729392. http://projecteuclid.org/euclid.aoms/1177729392.


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