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September, 1982 On the E-Optimality of PBIB Designs with a Small Number of Blocks
Gregory M. Constantine
Ann. Statist. 10(3): 1027-1031 (September, 1982). DOI: 10.1214/aos/1176345896


It is shown that several families of PBIB designs with relatively few blocks are $E$-optimal over the collection of all block designs. Among these are: the Partial Geometries with two associate classes; PBIB designs with $\lambda_1 = 1, \lambda_2 = 0$ and fewer blocks than varieties; PBIB designs with triangular schemes of size $n, \lambda_1 = 0, \lambda_2 = 1$ and block size $k \geq n/2$ (or $\lambda_1 = 1, \lambda_2 = 0$ and $k \geq n - 1)$; PBIB designs with $L_i$ schemes based on $\nu$ varieties with $\lambda_1 = 0, \lambda_2 = 1, k \geq \sqrt{\nu}$ (or $\lambda_1 = 1, \lambda_2 = 0$ and either $i - 1 \leq \sqrt{\nu} \leq k$ or $k \leq \sqrt{\nu} \leq i - 1$). The duals of these designs are also $E$-optimal. In certain settings Partial Geometries are the unique $E$-optimal designs.


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Gregory M. Constantine. "On the E-Optimality of PBIB Designs with a Small Number of Blocks." Ann. Statist. 10 (3) 1027 - 1031, September, 1982.


Published: September, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0489.62067
MathSciNet: MR663457
Digital Object Identifier: 10.1214/aos/1176345896

Primary: 62K05
Secondary: 62K10

Keywords: efficiency , eigenvalue , E-optimality , information matrix , partial geometry , PBIB design

Rights: Copyright © 1982 Institute of Mathematical Statistics


Vol.10 • No. 3 • September, 1982
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