| An approach to testing a multivariate distribution for ellipsoidal symmetry is suggested. The test statistics are defined as functionals of empirical processes indexed by special classes of functions. The parameters of the underlying distribution (the center of symmetry, the scaling transformation, etc.) are not supposed to be known and are estimated based on the data. General limit theorems for empirical processes that imply consistency of the tests against any asymmetric alternative (subject to some smoothness of the underlying density) and justify the use of a version of the bootstrap to evaluate the critical values of the test are proved. |
