## The Annals of Statistics

### Families of $A$-Optimal Block Designs for Comparing Test Treatments with a Control

#### Abstract

$A$-optimal designs for comparing each of $\nu$ test treatments simultaneously with a control, in $b$ blocks of size $k$ each are considered. It is shown that several families of BIB designs in the test treatments augmented by $t$ replications of a control in each block are $A$-optimal. In particular these designs with $t = 1$ are optimal whenever $(k - 2)^2 + 1 \leq \nu \leq (k - 1)^2$ irrespective of the number of blocks. This includes BIB designs associated with finite projective and Euclidean geometries.

#### Article information

Source
Ann. Statist., Volume 13, Number 2 (1985), 757-767.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176349552

Digital Object Identifier
doi:10.1214/aos/1176349552

Mathematical Reviews number (MathSciNet)
MR790570

Zentralblatt MATH identifier
0586.62113

JSTOR
Hedayat, A. S.; Majumdar, Dibyen. Families of $A$-Optimal Block Designs for Comparing Test Treatments with a Control. Ann. Statist. 13 (1985), no. 2, 757--767. doi:10.1214/aos/1176349552. https://projecteuclid.org/euclid.aos/1176349552