  We show that the balanced crossover designs given by Patterson [Biometrika 39
(1952) 32--48] are (a) universally optimal (UO) for the joint estimation of
direct and residual effects when the competing class is the class of connected
binary designs and (b) UO for the estimation of direct (residual) effects when
the competing class of designs is the class of connected designs (which
includes the connected binary designs) in which no treatment is given to the
same subject in consecutive periods. In both results, the formulation of UO is
as given by Shah and Sinha [Unpublished manuscript (2002)]. Further, we
introduce a functional of practical interest, involving both direct and
residual effects, and establish (c) optimality of Patterson's designs with
respect to this functional when the class of competing designs is as in (b)
above.
