September, 1952 Stochastic Estimation of the Maximum of a Regression Function

J. Kiefer, J. Wolfowitz

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 $n \rightarrow \infty$.

Citation

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

JOURNAL ARTICLE
5 PAGES

Vol.23 • No. 3 • September, 1952