Statistica Sinica 10(2000), 1091-1116

ON THE TYPE-1 OPTIMALITY OF NEARLY BALANCED

INCOMPLETE BLOCK DESIGNS WITH SMALL

CONCURRENCE RANGE

John P. Morgan and Sudesh K. Srivastav

Virginia Tech. and Tulane University

Abstract: The class of nearly balanced incomplete block designs with concurrence range , or NBBD(, is defined. This extends previous notions of ``most balanced'' designs to cover settings where off-diagonal entries of the concurrence matrix must differ by a positive integer . Sufficient conditions are found for optimality of NBBD(2)'s under type-1 criteria, then used to establish $A$- and $D$-optimality in settings where optimal designs were previously unknown. Some NBBD(3)'s are also found to be uniquely - and -optimal. Included is a study of settings where the necessary conditions for balanced incomplete block designs are satisfied, but no balanced design exists.

Key words and phrases: A-optimality, concurrence discrepancy, D-optimality, nearly balanced incomplete block design, semi-regular graph design.