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December, 1989 $A$-Optimal Weighing Designs when $N \equiv 3 (\operatorname{mod} 4)$
Y. S. Sathe, R. G. Shenoy
Ann. Statist. 17(4): 1906-1915 (December, 1989). DOI: 10.1214/aos/1176347401


In this paper we consider the problem of $A$-optimal weighing designs for $n$ objects in $N$ weighings on a chemical balance when $N \equiv 3(\operatorname{mod} 4)$. Let $D(N, n)$ denote the class of $N \times n$ design matrices $X_d$ whose elements are $+1$ and $-1$. It is shown that if $X_d$ is such that $X'_dX_d$ is a block matrix having a specified block structure, then $X_d$ is $A$-optimal in $D(N, n)$. It is found that in some cases the $A$-optimal design in $D(N, n)$ is not unique. A larger class of chemical balance weighing designs is $D^0(N, n)$, where $X_d$ may have some elements equal to zero. It is observed that the designs which are $A$-optimal in $D(N, n)$ are not necessarily $A$-optimal in $D^0(N, n)$.


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Y. S. Sathe. R. G. Shenoy. "$A$-Optimal Weighing Designs when $N \equiv 3 (\operatorname{mod} 4)$." Ann. Statist. 17 (4) 1906 - 1915, December, 1989.


Published: December, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0695.62190
MathSciNet: MR1026319
Digital Object Identifier: 10.1214/aos/1176347401

Primary: 62K05
Secondary: 62K15

Keywords: $A$-optimality , $D$-optimality , Block matrices , Hadamard matrices , weighing designs

Rights: Copyright © 1989 Institute of Mathematical Statistics


Vol.17 • No. 4 • December, 1989
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