Optimality of balanced uniform repeated measurements designs
The experiment of a repeated measurements design is based on n experimental units, t treatments and p periods and is denoted by \(\Omega_{t,n,p}\). It is shown that: i) If \(t=n=p\neq 2\) and if a balanced Latin square exists, this is universally optimal for the estimation of direct effects over \(\Omega_{t,t,t}\). ii) A balanced uniform design is universally optimal for the estimation of direct effects over \(\Omega_{t,2t,t}\) for \(t\geq 6.\) iii) If \(t=n=p\) and a design with given properties exists, then no balanced Latin square design can be universally optimal for the estimation of residual effects. Such an example is presented. iv) If \(n=t(t-1)\) an orthogonal residual effects design is universally optimal for the estimation of residual effects over \(\Omega_{t,n,t}\).
scientific article; zbMATH DE number 3866415