Optimal and efficient treatment control design in the heteroscedastic one-way layout with covariates

ABSTRACT

In this article, we take up the experimental situation of a heteroscedastic one-way layout model in the presence of a set of controllable covariates. For the joint estimation of the elementary contrasts of a set of test treatments with a control and the effects of covariates, sufficient conditions for the existence of an A-optimal design are identified. When these sufficient conditions are not met, we propose highly A-efficient designs. The methods of construction of A-optimal and highly A-efficient designs are discussed. For different values of the parameters of the design, A-efficiency of the proposed designs are tabulated for a comparative study.

KEYWORDS:

• One-way layout model
• covariates
• Hadamard matrix
• Kronecker product

AMS SUBJECT CLASSIFICATION (1970):

• 62K05

Acknowledgments

The authors sincerely thank the editor, the associate editor and two referees for their comments which have led to substantial improvement of the earlier version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.