Universal optimality of balanced uniform crossover designs

Abstract

Kunert [Ann. Statist. 12 (1984) 1006-1017] proved that, in the class of repeated measurement designs based on t treatments, p=t periods and $n=\lambda t$ experimental units, a balanced uniform design is universally optimal for direct treatment effects if $t \geq 3$ and $\lambda=1$, or if $t \geq 6$ and $\lambda=2$. This result is generalized to $t \geq 3$ as long as $\lambda \leq (t-1)/2$.