## The Annals of Statistics

### On the Optimality of Finite Williams II(a) Designs

#### Abstract

In this paper, we consider the type II(a) designs of Williams. It was shown, essentially, by Kiefer that the type II(a) designs are asymptotically universally optimum for a first order autoregression with parameter $\lambda > 0$. We concentrate on the stationary first order autoregression with $\lambda > 0$ and the extra plot version of the II(a) designs. Our main results are that the design is $D$- and $A$-optimal then, but is not necessarily $E$-optimal when $\lambda$ is small.

#### Article information

Source
Ann. Statist., Volume 15, Number 4 (1987), 1604-1628.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350613

Digital Object Identifier
doi:10.1214/aos/1176350613

Mathematical Reviews number (MathSciNet)
MR913577

Zentralblatt MATH identifier
0637.62071

JSTOR