Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series B, Pt. 1, pp. 128--141

MARGINALLY RESTRICTED CONSTRAINED OPTIMAL DESIGNS

By

MONG-NA HUANG and HSIU-FEN CHANG, National San Yat-sen University

SUMMARY.  In this paper, we consider the problem of constructing constrained optimal designs for regression models, when some of the factors are not under the control of the experimenters. That is more than one criterion are taken into consideration for finding the optimal designs with the distribution of the uncontrollable factor fixed in advance, where designs in the class with such restriction are referred to as merginally restricted designs. A necessary and sufficient condition for the merginally restricted optimal designs analogous to that of Lee (1988) for the unrestricted case is given. Then by using the condition, the equivalence theorem is derived, and for certain criteria it is used to establish relationships between the constrained optimal designs for the merginally restricted case through product designs, under some additive and Kronecker product kind of regression models.

AMS (1991) subject classification.  Primary 62K05, secondary 90C50.

Key words and phrases. Additive model, Fréchet derivative, Kronecker models, Lagrangian function, product designs.

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