  In repeated Measure Designs with multiple groups, the primary purpose is to
compare different groups in various aspects. For several reasons, the number of
measurements and therefore the dimension of the observation vectors can depend
on the group, making the usage of existing approaches impossible. We develop an
approach which can be used not only for a possibly increasing number of groups
$a$, but also for group-depending dimension $d_i$, which is allowed to go to
infinity. This is a unique high-dimensional asymptotic framework impressing
through its variety and do without usual conditions on the relation between
sample size and dimension. It especially includes settings with fixed
dimensions in some groups and increasing dimensions in other ones, which can be
seen as semi-high-dimensional. To find a appropriate statistic test new and
innovative estimators are developed, which can be used under these diverse
settings on $a,d_i$ and $n_i$ without any adjustments. We investigated the
asymptotic distribution of a quadratic-form-based test statistic and developed
an asymptotic correct test. Finally, an extensive simulation study is conducted
to investigate the role of the single group's dimension.
