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September, 1959 Complex Representation in the Construction of Rotatable Designs
R. C. Bose, R. L. Carter
Ann. Math. Statist. 30(3): 771-780 (September, 1959). DOI: 10.1214/aoms/1177706206


Response surface techniques are discussed as a generalization of factorial designs, emphasizing the concept of rotatability. It is shown that the necessary and sufficient conditions for a configuration of sample points to be a rotatable arrangement of a specified order are greatly simplified if, in the case of two factors, the factor space is considered as the complex plane. A theorem giving these conditions is proved, with an application to the conditions governing the combination of circular rotatable arrangements into configurations possessing a higher order of rotatability. This is done by showing that certain coefficients must vanish in the "design equation" whose roots are the (complex) values of the various sample points. A method is presented by which any configuration of sample points (for example, some configuration fixed by extra-statistical conditions) may be completed into a rotatable design of the first order by the addition of only two properly chosen further sample points.


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R. C. Bose. R. L. Carter. "Complex Representation in the Construction of Rotatable Designs." Ann. Math. Statist. 30 (3) 771 - 780, September, 1959.


Published: September, 1959
First available in Project Euclid: 27 April 2007

zbMATH: 0231.62091
MathSciNet: MR108873
Digital Object Identifier: 10.1214/aoms/1177706206

Rights: Copyright © 1959 Institute of Mathematical Statistics

Vol.30 • No. 3 • September, 1959
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