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Universal optimality of experimental designs: Definitions and a criterion
Author(s) -
Bondar James V.
Publication year - 1983
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314890
Subject(s) - eigenvalues and eigenvectors , optimality criterion , set (abstract data type) , optimal design , mathematics , matrix (chemical analysis) , regular polygon , mathematical optimization , computer science , algebra over a field , pure mathematics , statistics , physics , materials science , geometry , quantum mechanics , composite material , programming language
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.