On the optimality of block designs
type: Item
instance of: scholarly article
title: On the optimality of block designs
zbMATH Open document ID: 0588.62123
published in: Annals of the Institute of Statistical Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A family of highly efficient designs in the sense of the E-criterion is described. These designs have strictly better E-performance than regular graph designs, yet the off-diagonal entries of their C-matrix differ by as much as two. Some counterexamples to conjectures in experimental design are then supplied. Asymptotic behavior and equivalence of the A- and D-criteria under a certain condition of uniqueness are analyzed as well.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62K10
zbMATH DE Number: 3945149
zbMATH Keywords: E-optimality
zbMATH Keywords: A-optimality
zbMATH Keywords: D-optimality
zbMATH Keywords: eigenvalue
zbMATH Keywords: positive definite matrix
zbMATH Keywords: line graph
zbMATH Keywords: spanning tree
zbMATH Keywords: E-criterion
zbMATH Keywords: regular graph designs
zbMATH Keywords: counterexamples
zbMATH Keywords: Asymptotic behavior
zbMATH Keywords: equivalence of the A- and D- criteria
author: Gregory M. Constantine
MaRDI profile type: Publication
cites work: Line graphs, root systems, and elliptic geometry
cites work: On the efficiency of regular generalized line graph designs
cites work: Do nearly balanced multigraphs have more spanning trees?
cites work: On spectral characterization and embeddings of graphs
cites work: Q4124844
cites work: Q3953028
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cites work: Circuits and efficiency in incomplete block designs
cites work: Q5789039
description: scientific article; zbMATH DE number 3945149