A Lower Bound to the Measure of Optimality for Main Effect Plans in the Symmetric Factorial Experiments

• Published in: Communications in statistics. Theory and methods Vol. 40; no. 13; pp. 2358 - 2365
• Main Authors: Chatterjee, K., Evangelaras, H., Koukouvinos, C.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 21.04.2011; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Combinatorics; Combinatorics. Ordered structures; Designs and configurations; Exact sciences and technology; Experimental design; General topics; Lower bounds; Mathematical models; Mathematics; MS-optimality; Multivariate analysis; Operations research; Optimization; Orthogonal arrays; Primary 62K15; Probability and statistics; Queuing theory; Sciences and techniques of general use; Secondary 05B20; Stands; Statistics; Strength; Studies; Supports; Trace; Lower bound; Factor analysis; Orthogonal array; Statistical theory; Secondary 05B20; Primary 62K15; Multivariate analysis; Information matrix; MS-optimality; Statistical method; Trace; Information measure; Correspondence analysis; Experimental design; Factorial design; Principal component analysis; Information theory; Orthogonal arrays
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610921003778233

A design d is called D-optimal if it maximizes det(M d ), and is called MS-optimal if it maximizes tr(M d ) and minimizes tr[(M d ) 2 ] among those which maximize tr(M d ), where M d stands for the information matrix produced from d under a given model. In this article, we establish a lower bound for tr[(M d ) 2 ] with respect to a main effects model, where d is an s-level symmetric orthogonal array of strength at least one. Non isomorphic two level MS-optimal orthogonal arrays of strength one with N = 10, 14, and 18 runs, non isomorphic three level MS-optimal orthogonal arrays of strength one with N = 6, 12, and 15 runs and non isomorphic four level MS-optimal orthogonal arrays of strength one with N = 12 runs are also presented.