Optimality aspects of 3-concurrence most balanced designs |
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Institution: | Department of Statistics and Actuarial Science, University of Waterloo, Canada N2L 3G1 |
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Abstract: | Takcuchi (1961,1963) established E-optimality of Group Divisible Designs (GDDs) with λ2=λ1+1. Much later, Cheng (1980) and Jacroux (1980,1983) demonstrated E-optimality property of the GDDs with n=2,λ1=λ2+1 or with m=2,λ2=λ1+2. The purpose of this paper is to provide a unified approach for identifying certain classes of designs as E-optimal. In the process, we come up with a complete characterization of all E-optimal designs attaining a specific bound for the smallest non-zero eigenvalue of the underlying C-matrices. This establishes E-optimality of a class of 3-concurrence most balanced designs with suitable intra- and inter-group balancing. We also discuss the MV-optimality aspect of such designs. |
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