  The statistics of critical wave functions at the Anderson transition in three
and four dimensions are studied numerically. The distribution of the inverse
participation ratios (IPR) $P_q$ is shown to acquire a scale-invariant form in
the limit of large system size. Multifractality spectra governing the scaling
of the ensemble-averaged IPRs are determined. Conjectures concerning the IPR
statistics and the multifractality at the Anderson transition in a high spatial
dimensionality are formulated.
