The Annals of Statistics

Construction Methods for $D$-Optimum Weighing Designs when $n \equiv 3 (\operatorname{mod} 4)$

Z. Galil and J. Kiefer

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Abstract

In the setting where the weights of $k$ objects are to be determined in $n$ weighings on a chemical balance (or equivalent problems), for $n \equiv 3 (\operatorname{mod} 4)$, Ehlich and others have characterized certain "block matrices" $C$ such that, if $X'X = C$ where $X(n \times k)$ has entries $\pm1$, then $X$ is an optimum design for the weighing problem. We give methods here for constructing $X$'s for which $X'X$ is a block matrix, and show that it is the optimum $C$ for infinitely many $(n, k)$. A table of known constructibility results for $n < 100$ is given.

Article information

Source
Ann. Statist., Volume 10, Number 2 (1982), 502-510.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345791

Digital Object Identifier
doi:10.1214/aos/1176345791

Mathematical Reviews number (MathSciNet)
MR653525

Zentralblatt MATH identifier
0489.62068

JSTOR
links.jstor.org

Subjects
Primary: 62K15: Factorial designs
Secondary: 05B20: Matrices (incidence, Hadamard, etc.)

Keywords
62K5 Optimum designs weighing designs construction methods $D$-optimality first order designs fractional factorials

Citation

Galil, Z.; Kiefer, J. Construction Methods for $D$-Optimum Weighing Designs when $n \equiv 3 (\operatorname{mod} 4)$. Ann. Statist. 10 (1982), no. 2, 502--510. doi:10.1214/aos/1176345791. https://projecteuclid.org/euclid.aos/1176345791


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