Testing hypotheses about covariance matrices in general MANOVA designs

We introduce a unified approach for testing variety of rather general null hypotheses that can be formulated in terms covariance matrices. These include as special cases, example, equal variances, traces, or elements the matrix taking certain values. The proposed method only requires very few assumptions and thus promises to broad practical use. Different test statistics are defined, their asymptotic approximate sampling distributions derived. In order particularly improve small-sample behaviour resulting tests, two bootstrap-based methods developed theoretically justified. Several simulations shed light on performance tests. analysis real data set illustrates application procedures.