The Annals of Statistics

Optimal repeated measurements designs: the linear optimality equations

H. B. Kushner

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In approximate design theory, necessary and sufficient conditions that a repeated measurements design be universally optimal are given as linear equations whose unknowns are the proportions of subjects on the treatment sequences. Both the number of periods and the number of treatments in the designs are arbitrary, as is the covariance matrix of the normal response model. The existence of universally optimal "symmetric" designs is proved; the single linear equation which the proportions satisfy is given. A formula for the information matrix of a universally optimal design is derived.

Article information

Ann. Statist., Volume 25, Number 6 (1997), 2328-2344.

First available in Project Euclid: 30 August 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs
Secondary: 62K10: Block designs

Optimal repeated measurements designs universal optimality treatment effect carryover effect treatment sequence


Kushner, H. B. Optimal repeated measurements designs: the linear optimality equations. Ann. Statist. 25 (1997), no. 6, 2328--2344. doi:10.1214/aos/1030741075.

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