Block designs for first and second order neighbor correlations
type: Item
instance of: scholarly article
title: Block designs for first and second order neighbor correlations
zbMATH Open document ID: 0664.62078
author: J. P. Morgan
author: I. M. Chakravarti
published in: The Annals of Statistics
publication date: 1988-01-01T00:00:00Z
review text: Constructions and optimality results are given for block designs under first and second order (NN1 and NN2, respectively) neighbor correlations, extending the work of \textit{J. Kiefer} and \textit{H. P. Wynn} [ibid. 9, 737- 757 (1981; Zbl 0546.62051)]. Conditions for optimality and minimality are given for the NN2 model and new minimality results are found for the NN1 case. Construction of NN2 optimum complete block designs is solved and combinatorial arrays are used for NN2 optimum incomplete block esigns. In many cases these are minimum optimum NN1 designs as well. A new solution for block size 3 is given. A method for constructing NN1 designs with partial variance balance is introduced and several series of these designs are shown to enjoy weaker optimality properties.
Mathematics Subject Classification ID: 62K10
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 4086808
zbMATH Keywords: Hamiltonian cycles
zbMATH Keywords: semibalanced arrays
zbMATH Keywords: transitive arrays
zbMATH Keywords: neighbor correlations
zbMATH Keywords: minimality
zbMATH Keywords: NN2 optimum complete block designs
zbMATH Keywords: NN2 optimum incomplete block esigns
zbMATH Keywords: minimum optimum NN1 designs
zbMATH Keywords: new solution for block size 3
zbMATH Keywords: partial variance balance
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350956
OpenAlex ID: W1974587881
DOI: 10.1214/AOS/1176350956
description: scientific article; zbMATH DE number 4086808