The Annals of Statistics

Optimal repeated measurements designs: the linear optimality equations

H. B. Kushner

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Abstract

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

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

Dates
First available in Project Euclid: 30 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1030741075

Digital Object Identifier
doi:10.1214/aos/1030741075

Mathematical Reviews number (MathSciNet)
MR1604457

Zentralblatt MATH identifier
0894.62088

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

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

Citation

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


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References

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  • ORANGEBURG, NEW YORK 10962 E-MAIL: kushner@rfmh.org