## The Annals of Statistics

### Lower Rate of Convergence for Locating a Maximum of a Function

Hung Chen

#### Abstract

The problem is considered of estimating the point of global maximum of a function $f$ belonging to a class $F$ of functions on $\lbrack -1, 1 \rbrack,$ based on estimates of function values at points selected possibly during the experimentation. If $p$ is odd and greater than 1, $K$ is a positive constant and $F$ contains enough functions with $p$th derivatives bounded by $K$, then we prove that, under additional weak regularity conditions, the lower rate of convergence is $n^{-(p - 1)/(2p)}$.

#### Article information

Source
Ann. Statist., Volume 16, Number 3 (1988), 1330-1334.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350965

Digital Object Identifier
doi:10.1214/aos/1176350965

Mathematical Reviews number (MathSciNet)
MR959206

Zentralblatt MATH identifier
0651.62034

JSTOR

Subjects
Primary: 62G99: None of the above, but in this section
Secondary: 62L20: Stochastic approximation

#### Citation

Chen, Hung. Lower Rate of Convergence for Locating a Maximum of a Function. Ann. Statist. 16 (1988), no. 3, 1330--1334. doi:10.1214/aos/1176350965. https://projecteuclid.org/euclid.aos/1176350965