Testing for affine equivalence of elliptically symmetric distributions

Let <f>X</f> and <f>Y</f> be <f>d</f>-dimensional random vectors having elliptically symmetric distributions. Call <f>X</f> and <f>Y</f> affinely equivalent if <f>Y</f> has the same distribution as <f>AX+b</f> for some nonsingular <f>d×d</f>-matrix <f>A</f> and some <f>b∈Rd</f>. 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. [Copyright &y& Elsevier]