Some Universally Optimal Row-Column Designs with Empty Nodes
基于作者先前工作，推导了行列设计的简化系数矩阵和方差分析一般形式，用于识别具有空节点的行列设计的理想性质。构造了三类特殊设计并证明其在指定参数下是通用最优的。
General forms of the reduced coefficient matrix for estimation of treatment effects and the intrablock analysis of variance of row-column designs with n experimental units and v treatments are obtained from earlier work by the authors. These results are used to identify desirable properties for row-column designs with empty nodes. A need for such designs is apparent when the blocking criteria are implemented in sequence and empty nodes do not represent wasted experimental units. The construction and properties of three special classes of row-column designs with some empty nodes are discussed and examples given. In particular, it is shown that, if a row-column design belongs to one of these classes, then it is universally optimal for specified design parameters, where universally optimal designs are designs that maximize a generalized optimality criterion as defined by Kiefer.