Optimal tests for elliptical symmetry: Specified and unspecified location

Although the assumption of elliptical symmetry is quite common in multivariate analysis and widespread a number applications, problem testing null hypothesis ellipticity so far has not been addressed fully satisfactory way. Most papers literature indeed are dealing with specified location actually address rather than non-elliptical alternatives. In this paper, we proposing new classes procedures, both for unspecified location. The backbone our construction Le Cam’s asymptotic theory statistical experiments, optimality to be understood locally asymptotically within family generalized skew-elliptical distributions. tests enjoying all desirable properties “good” test symmetry: they have simple distributions under entire radial density shape parameter; affine-invariant, computationally fast, intuitively understandable, too demanding terms moments. While achieving against alternatives, remain powerful much broader class significantly outperform available competitors.