Designs with partial neighbour balance
type: Item
instance of: scholarly article
title: Designs with partial neighbour balance
zbMATH Open document ID: 0575.62070
DOI: 10.1016/0378-3758(85)90052-7
author: Deborah J. Street
author: Anne Penfold Street
published in: Journal of Statistical Planning and Inference
publication date: 1985-01-01T00:00:00Z
review text: A nearest neighbour (NN) design may be one-dimensional, with blocks ordered either cyclically or linearly, or it may be a two-dimensional rectangular array (row and column design), regarded as linear in each direction or as being on a torus. A one-dimensional design is said to have exact m-th-level NN balance if and only if all unordered pairs of distinct treatments occur as m-th nearest neighbours equally often, say \(\lambda_ m\) times. (The authors also define partial m-th level NN balance). This paper is motivated by the observation of \textit{G. N. Wilkinson}, \textit{S. R. Eckert}, \textit{T. W. Hancock} and \textit{O. Mayo} (see the preceding entry, Zbl 0575.62069) that efficiency is enhanced for 2-replicate designs when for any pair of treatments their lists of neighbours (to a specified level) has at most one element in common. This paper gives several constructions for designs which satisfy this balance property of Wilkinson et al.
Mathematics Subject Classification ID: 62K10
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 3919591
zbMATH Keywords: nearest neighbour balance
zbMATH Keywords: partial nearest neighbour balance
zbMATH Keywords: equi- neighboured BIBD
zbMATH Keywords: orthogonal Latin square
zbMATH Keywords: complete Latin square
zbMATH Keywords: nearest neighbour (NN) design
reviewed by: Jennifer Seberry
MaRDI profile type: Publication
full work available at URL: 0378-3758(85)90052-7
OpenAlex ID: W2029748834
cites work: Q4179702
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description: scientific article; zbMATH DE number 3919591