## The Annals of Mathematical Statistics

### Stochastic Approximation for Smooth Functions

Vaclav Fabian

#### Abstract

The problem of approximating a point $\theta$ of minimum of a function $f \varepsilon \mathscr{C}$ (see 2.1) is considered. An approximation procedure of the type described in Fabian (1967) using the design described in Fabian (1968), but with the size of design increasing, achieves the speed \begin{equation*}\tag{1}E|X_n - \theta|^2 = o(t^{-1}_n \log ^3 t_n);\end{equation*} here $X_n$ is the $n$th approximation and $t_n$ the number of observations necessary to construct $X_1, X_2, \cdots, X_n$.

#### Article information

Source
Ann. Math. Statist., Volume 40, Number 1 (1969), 299-302.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177697825

Digital Object Identifier
doi:10.1214/aoms/1177697825

Mathematical Reviews number (MathSciNet)
MR235655

Zentralblatt MATH identifier
0193.15503

JSTOR