Statistica Sinica 13(2003), 1147-1163

STANDARDIZED MAXIMIN $\mbf E$-OPTIMAL DESIGNS FOR

THE MICHAELIS-MENTEN MODEL

Holger Dette$^1$, Viatcheslav B. Melas$^2$ and Andrey Pepelyshev$^2$

$^1$Ruhr-Universität Bochum and $^2$St. Petersburg State University

Abstract: In the Michaelis-Menten model we determine efficient designs by maximizing a minimum of standardized $E$-efficiencies. It is shown in many cases that optimal designs are supported at only two points and that the support points and corresponding weights can be characterized explicitly. Moreover, a numerical study indicates that two point designs are usually very efficient, even if they are not optimal. Some practical recommendations for the design of experiments in the Michaelis-Menten model are given.

Key words and phrases: Chebyshev system, E-optimal designs, Michaelis-Menten model, minimax-optimality, standardized optimal designs.