Designs in the Presence of Trends
Model: Fixed effects model for block designs with a first degree trend term specific to every block Optimality criteria: Universal optimality (UO) Major tools: Semi balanced arrays, Kiefer’s proposition 1 Optimality results: Classes of UO designs both within restricted subclasses and within the unrestricted class of designs Thrust: Combinatorial arrangement of treatments within each block of a BIBD so that the trend-adjusted C-matrix has maximal trace and completely symmetric structure
In this Chapter we consider a model for a block design where in addition to the block and treatment effect parameters, there is a linear trend term specific to every block. We first give designs which are optimal within the class of binary designs or within the class of trend free designs. We also give designs which are optimal within the unrestricted class. In all cases, we obtain trend-adjusted C-matrices which are completely symmetric and have maximal trace so that the designs are universally optimal. Semi balanced arrays of Rao are found very useful in this connection.
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