Testing for affine equivalence of elliptically symmetric distributions

Let X and Y be d-dimensional random vectors having elliptically symmetric distributions. Call X and Y affinely equivalent if Y has the same distribution as AX+b for some nonsingular d×d-matrix A and some b∈Rd. This paper studies a class of affine invariant tests for affine equivalence under certain moment restrictions. The test statistics are measures of discrepancy between the empirical distributions of the norm of suitably standardized data.