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Optimal repeated measurements designs: The linear optimality equations. (English) Zbl 0894.62088

Ann. Stat. 25, No. 6, 2328-2344 (1997); correction ibid. 26, No. 5, 2081 (1998).
Summary: 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.

MSC:

62K05 Optimal statistical designs
62K10 Statistical block designs
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