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Statistica Sinica 27 (2017), 1-22

ON OPTIMALITY AND CONSTRUCTION OF CIRCULAR
REPEATED-MEASUREMENTS DESIGNS
R. A. Bailey1,2 , Peter J. Cameron1,2 , Katarzyna Filipiak3 , Joachim Kunert4 and Augustyn Markiewicz5
1University of St Andrews, 2University of London,
3Poznań University of Technology,4TU Dortmund University and
5Poznań University of Life Sciences

Abstract: The aim of this paper is to characterize and construct universally optimal designs among the class of circular repeated-measurements designs when the parameters do not permit balance for carry-over effects. It is shown that some circular weakly neighbour balanced designs defined by Filipiak and Markiewicz (2012) are universally optimal repeated-measurements designs. These results extend the work of Magda (1980), Kunert (1984b), and Filipiak and Markiewicz (2012).

Key words and phrases: Circular weakly balanced design, repeated-measurements design, uniform design, universal optimality.

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