  Statisticians increasingly face the problem to reconsider the adaptability of
classical inference techniques. In particular, divers types of high-dimensional
data structures are observed in various research areas; disclosing the
boundaries of conventional multivariate data analysis. Such situations occur,
e.g., frequently in life sciences whenever it is easier or cheaper to
repeatedly generate a large number $d$ of observations per subject than
recruiting many, say $N$, subjects. In this paper we discuss inference
procedures for such situations in general heteroscedastic split-plot designs
with $a$ independent groups of repeated measurements. These will, e.g., be able
to answer questions about the occurrence of certain time, group and
interactions effects or about particular profiles.
  The test procedures are based on standardized quadratic forms involving
suitably symmetrized U-statistics-type estimators which are robust against an
increasing number of dimensions $d$ and/or groups $a$. We then discuss its
limit distributions in a general asymptotic framework and additionally propose
improved small sample approximations. Finally its small sample performance is
investigated in simulations and the applicability is illustrated by a real data
analysis.
