Optimality aspects of 3-concurrence most balanced designs

• Published in: Journal of statistical planning and inference Vol. 20; no. 2; pp. 229 - 236
• Main Authors: Sinha, B.K., Shah, K.R.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 1988
• Subjects: E-optimality; group divisible designs; intra- and inter-group balanced block designs; group divisible designs; intra- and inter-group balanced block designs; E-optimality; 62K05; 62K10
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/0378-3758(88)90127-9

Takcuchi (1961,1963) established E-optimality of Group Divisible Designs (GDDs) with λ 2= λ 1+1. Much later, Cheng (1980) and Jacroux (1980,1983) demonstrated E-optimality property of the GDDs with n=2, λ 1= λ 2+1 or with m=2, λ 2= λ 1+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.