## The Annals of Statistics

### Optimality of Certain Asymmetrical Experimental Designs

Ching-Shui Cheng

#### Abstract

The problem of finding an optimal design for the elimination of one-way heterogeneity when a balanced block design does not exist is studied. A general result on the optimality of certain asymmetrical designs is proved and applied to the block design setting. It follows that if there is a group divisible partially balanced block design (GD PBBD) with 2 groups and $\lambda_2 = \lambda_1 + 1$, then it is optimal w.r.t. a very general class of criteria including all the commonly used ones. On the other hand, if there is a GD PBBD with 2 groups and $\lambda_1 = \lambda_2 + 1$, then it is optimal w.r.t. another class of criteria. Uniqueness of optimal designs and some other miscellaneous results are also obtained.

#### Article information

Source
Ann. Statist. Volume 6, Number 6 (1978), 1239-1261.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176344371

JSTOR

Digital Object Identifier
doi:10.1214/aos/1176344371

Mathematical Reviews number (MathSciNet)
MR523760

Zentralblatt MATH identifier
0396.62055

Subjects
Primary: 62K05: Optimal designs
Secondary: 62K10: Block designs

#### Citation

Cheng, Ching-Shui. Optimality of Certain Asymmetrical Experimental Designs. The Annals of Statistics 6 (1978), no. 6, 1239--1261. doi:10.1214/aos/1176344371. http://projecteuclid.org/euclid.aos/1176344371.