B1084
Title: On the power of Sobolev tests for isotropy under local rotationally symmetric alternatives
Authors: Thomas Verdebout - Universite Libre de Bruxelles (Belgium) [presenting]
Eduardo Garcia-Portugues - Carlos III University of Madrid (Spain)
Davy Paindaveine - Universite libre de Bruxelles (Belgium)
Abstract: One of the most classical problems in multivariate statistics is considered, namely, the problem of testing isotropy, or equivalently, the problem of testing uniformity on the unit hypersphere. Rather than restricting to tests that can detect specific types of alternatives only, we consider the broad class of Sobolev tests. While these tests are known to allow for omnibus testing of uniformity, their non-null behavior and consistency rates, unexpectedly, remain largely unexplored. To improve on this, we thoroughly study the local asymptotic powers of Sobolev tests under the most classical alternatives to uniformity, namely, under rotationally symmetric alternatives. We show in particular that the consistency rate of Sobolev tests does not only depend on the coefficients defining these tests but also on the derivatives of the underlying angular function at zero.
