Universal optimality of experimental designs: Definitions and a criterion
- 18 December 1983
- journal article
- Published by Wiley in The Canadian Journal of Statistics / La Revue Canadienne de Statistique
- Vol. 11 (4) , 325-331
- https://doi.org/10.2307/3314890
Abstract
Several definitions of universal optimality of experimental designs are found in the Literature; we discuss the interrelations of these definitions using a recent characterization due to Friedland of convex functions of matrices. An easily checked criterion is given for a design to satisfy the main definition of universal optimality; this criterion says that a certain set of linear functions of the eigenvalues of the information matrix is maximized by the information matrix of a design if and only if that design is universally optimal. Examples are given; in particular we show that any universally optimal design is (M, S)‐optimal in the sense of K. Shah.Keywords
This publication has 9 references indexed in Scilit:
- Sur quelques applications des fonctions convexes et concaves au sens de I. SchurPublished by Springer Nature ,1984
- Optimum continuous block designsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1981
- Convex spectral functionsLinear and Multilinear Algebra, 1981
- The interplay of optimality and combinatorics in experimental designThe Canadian Journal of Statistics / La Revue Canadienne de Statistique, 1981
- Optimality of Some Weighing and $2^n$ Fractional Factorial DesignsThe Annals of Statistics, 1980
- Optimality of Certain Asymmetrical Experimental DesignsThe Annals of Statistics, 1978
- Droplet ChondrulesScience, 1975
- General Equivalence Theory for Optimum Designs (Approximate Theory)The Annals of Statistics, 1974
- Optimum Experimental DesignsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1959