Semiparametrically efficient rank-based inference for shape. I. optimal rank-based tests for sphericity

We propose a class of rank-based procedures for testing that the shape matrix V of an elliptical distribution (with unspecified center of symmetry, scale and radial density) has some fixed value V-0; this includes, for V-0 = I-k, the problem of testing for sphericity as an important particular case. The proposed tests are invariant under ...More