Elfving's Theorem for $D$-Optimality

The Phelps–Koopmans theorem and potential optimality

The Phelps–Koopmans theorem states that if every limit point of a path of capital stocks exceeds the “golden rule,” then that path is inefficient: there is another feasible path from the same initial stock that provides at least as much consumption at every date and strictly more consumption at some date. I show that in a model with nonconvex technologies and preferences, the theorem is false i...

Equivalence theorem for Schur optimality of experimental designs

An experimental design is said to be Schur optimal, if it is optimal with respect to the class of all Schur isotonic criteria, which includesKiefer’s criteria of p-optimality, distance optimality criteria andmany others. In the paper we formulate an easily verifiable necessary and sufficient condition for Schur optimality in the set of all approximate designs of a linear regression experiment w...

A Fixed Point Theorem in Generalized D-metric Spaces

Comparison of Spectral and Hadamard Bounds for D-Optimality

We introduce a spectral bound for D-optimal design problems, based on singular values. We compare the spectral bound to a bound based on Hadamard's inequality which was introduced by Welch. In particular, we demonstrate that (i) in general, neither bound dominates the other, (ii) the spectral bound is superior in a general situation of highly replicated designs, and (iii) the spectral bound is ...

Augmenting supersaturated designs with Bayesian D-optimality

Amethodology is developed to add runs to existing supersaturated designs. The technique uses information from the analysis of the initial experiment to choose the best possible follow-up runs. After analysis of the initial data, factors are classified into one of three groups: primary, secondary, and potential. Runs are added to maximize a Bayesian D-optimality criterion to increase the informa...