E-optimal and highly E-efficient designs with (mod 4) correlated observations

Abstract

The present paper analyses the linear model with design matrices with elements in or in assuming the existence of correlated errors with a known correlation structure. This model corresponds to the model of three- or two-level factorial design or to the model of chemical balance weighing design. The most difficult case when the number of observations is considered. The E-optimal and the highly E-efficient designs and their constructions are presented separately for 1, 2, 3 and more than three parameters. It is also shown that these designs are not A- and D-optimal for many values of the number of observations and the number of parameters.

Keywords:

• A-
• D-optimality
• chemical balance weighing design
• correlation
• E-optimal design
• factorial design
• highly E-efficient design

AMS Subject Classifications:

• 62K05
• 15A18

Acknowledgements

The author is grateful to an anonymous referee for valuable comments and constructive suggestions.

Notes

No potential conflict of interest was reported by the author.

Supplemental data for this article can be accessed here. [http://dx.doi.org/10.1080/03081087.2016.1272542]