Asymptotic optimality of a class of rank tests for replicated Latin-square designs

This paper is concerned with the class of conditionally distribution-free rank tests introduced by Monga and Tardif (1994) for replicated Latin square designs. It is possible to proceed with an enlargement of this class by making use of the method of ranking after substitution. The unconditional asymptotic behaviour of any member of the enlarged class is derived under the null hypothesis of no treatment as well as under a sequence of contiguous alternatives. This enables the establishment of the asymptotic Pitman efficiency of any member relative to the asymptotically minimax test and to conclude that at least one member of the class is asymptotically as efficient as the latter.