The Annals of Statistics

On the Optimality of Finite Williams II(a) Designs

J. Kunert and R. J. Martin

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62K05: Optimal designs
Secondary: 62K10: Block designs 62P10: Applications to biology and medical sciences

Keywords
Autoregression correlated errors experimental design optimal design $\varphi_p$-criteria

Citation

Kunert, J.; Martin, R. J. On the Optimality of Finite Williams II(a) Designs. Ann. Statist. 15 (1987), no. 4, 1604--1628. doi:10.1214/aos/1176350613. https://projecteuclid.org/euclid.aos/1176350613


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