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In this paper, the sufficient condition for the E-optimality of PBB designs with two associate classes is given. This condition is expressed in terms of the parameters of design and their incidence matrix. In particular, the £-optimality criterion for equireplicated designs with binary incidence matrix is given. In this case, we can express the £-optimality criterion in terms of parameters of design only. Finally, we characterized the contrasts of treatment which determine the F-optimality of design....
We suggest in this paper a method for assessing the validity of the assumption of normal distribution of random errors in a two-factor split-plot design. The vector observation is transformed into residual vector and then the residual vector is tranformed into an adjusted residual vector from the least squares method by linear transformation. Since the components of the adjusted residual vector satisfy the conditions for a simple sample, therefore the appropriately chosen adjusted residual vector...
An investigation of the consistency of a linear inequality system is considered. It is proven that the system of linear inequalities Ax≥b is consistent if and only if for any generalized inverse A− of a matrix A the system of equations (I−AA−)v=−(I−AA−)b has a nonnegative solution for the vector v. Consistency of the above system does not depend on the choice of the matrix A−. The paper also presents methods for investigating the existence of nonnegative solutions of systems of linear equations.
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